Search: a102338 -id:a102338
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A007811
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Numbers k for which 10k+1, 10k+3, 10k+7 and 10k+9 are primes.
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+10
51
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1, 10, 19, 82, 148, 187, 208, 325, 346, 565, 943, 1300, 1564, 1573, 1606, 1804, 1891, 1942, 2101, 2227, 2530, 3172, 3484, 4378, 5134, 5533, 6298, 6721, 6949, 7222, 7726, 7969, 8104, 8272, 8881, 9784, 9913, 10111, 10984, 11653, 11929, 12220, 13546, 14416, 15727
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OFFSET
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1,2
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LINKS
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FORMULA
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MAPLE
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for n from 1 to 10000 do m := 10*n: if isprime(m+1) and isprime(m+3) and isprime(m+7) and isprime(m+9) then print(n); fi: od: quit
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MATHEMATICA
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Select[ Range[ 1, 10000, 3 ], PrimeQ[ 10*#+1 ] && PrimeQ[ 10*#+3 ] && PrimeQ[ 10*#+7 ] && PrimeQ[ 10*#+9 ]& ]
Select[Range[15000], And @@ PrimeQ /@ ({1, 3, 7, 9} + 10#) &] (* Ray Chandler, Jan 12 2007 *)
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PROG
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(Magma) [n: n in [0..10000] | forall{10*n+r: r in [1, 3, 7, 9] | IsPrime(10*n+r)}]; // Bruno Berselli, Sep 04 2012
(PARI) p=2; q=3; r=5; forprime(s=7, 1e5, if(s-p==8 && r-p==6 && q-p==2 && p%10==1, print1(p", ")); p=q; q=r; r=s) \\ Charles R Greathouse IV, Mar 21 2013
(Haskell)
a007811 n = a007811_list !! (n-1)
a007811_list = map (pred . head) $ filter (all (== 1) . map a010051') $
iterate (zipWith (+) [10, 10, 10, 10]) [1, 3, 7, 9]
(Perl) use ntheory ":all"; my @s = map { ($_-1)/10 } sieve_prime_cluster(10, 1e9, 2, 6, 8); say for @s; # Dana Jacobsen, May 04 2017
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CROSSREFS
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Cf. A024912, A102338, A102342, A102700, A007530, A014561, A008471, A032352, A216292, A216293, A125855.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A030431
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Primes of form 10n+3.
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+10
48
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3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263, 283, 293, 313, 353, 373, 383, 433, 443, 463, 503, 523, 563, 593, 613, 643, 653, 673, 683, 733, 743, 773, 823, 853, 863, 883, 953, 983, 1013, 1033, 1063, 1093, 1103, 1123, 1153, 1163, 1193
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OFFSET
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1,1
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COMMENTS
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Also primes of form 5n+3.
Primes p such that arithmetic mean of divisors of p^4 is an integer. There are 2 such sequences of primes, this one and A030430. - Ctibor O. Zizka, Oct 20 2009
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LINKS
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FORMULA
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MATHEMATICA
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Select[Prime@Range[200], Mod[ #, 10] == 3 &] (* Ray Chandler, Nov 07 2006 *)
Select[10 Range[0, 150] + 3, PrimeQ] (* Harvey P. Dale, Apr 06 2011 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A023238
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Primes p such that 10*p + 3 is also prime.
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+10
7
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2, 5, 7, 11, 17, 19, 23, 29, 31, 37, 43, 59, 61, 67, 73, 101, 103, 109, 137, 149, 173, 191, 193, 197, 199, 211, 227, 229, 233, 239, 263, 269, 271, 283, 331, 337, 353, 359, 367, 373, 379, 383, 401, 409, 449, 467, 479, 499, 523, 541, 557, 569, 607, 613, 617, 647, 673, 683
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OFFSET
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1,1
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LINKS
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MAPLE
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MATHEMATICA
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Select[Prime[Range[200]], PrimeQ[10# + 3] &] (* Alonso del Arte, Jun 24 2014 *)
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PROG
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(Magma) [n: n in [0..1000] | IsPrime(n) and IsPrime(10*n+3)] // Vincenzo Librandi, Nov 20 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A049508
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Numbers k such that prime(k) == 3 (mod 10).
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+10
7
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2, 6, 9, 14, 16, 21, 23, 27, 30, 38, 40, 44, 48, 51, 56, 61, 62, 65, 71, 74, 76, 84, 86, 90, 96, 99, 103, 108, 112, 117, 119, 122, 124, 130, 132, 137, 143, 147, 150, 153, 162, 166, 170, 174, 179, 183, 185, 188, 191, 192, 196, 198, 200, 208, 213, 220, 224, 227, 231
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OFFSET
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1,1
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COMMENTS
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The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021
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LINKS
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FORMULA
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MATHEMATICA
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Select[Range[240], Mod[Prime[ # ], 10] == 3 &] (* Ray Chandler, Nov 07 2006 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A023269
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Primes that remain prime through 2 iterations of function f(x) = 10x + 3.
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+10
1
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2, 7, 17, 19, 23, 37, 61, 67, 73, 101, 103, 173, 193, 233, 359, 383, 409, 479, 541, 557, 607, 613, 719, 809, 857, 997, 1013, 1033, 1109, 1117, 1237, 1297, 1361, 1459, 1531, 1549, 1699, 1823, 1871, 1979, 1999, 2069, 2131, 2161, 2347, 2377, 2399, 2447, 2663
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OFFSET
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1,1
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COMMENTS
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Primes p such that 10*p+3 and 100*p+33 are also primes. - Vincenzo Librandi, Aug 04 2010
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LINKS
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MATHEMATICA
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Select[Prime@ Range@ 400, Times @@ Boole@ PrimeQ@ Rest@ NestList[10 # + 3 &, #, 2] > 0 &] (* Michael De Vlieger, Sep 16 2016 *)
Select[Prime[Range[500]], AllTrue[Rest[NestList[10#+3&, #, 2]], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 03 2018 *)
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PROG
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(Magma) [n: n in [1..100000] | IsPrime(n) and IsPrime(10*n+3) and IsPrime(100*n+33)] // Vincenzo Librandi, Aug 04 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A153403
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Numbers n such that 10*n+3 is not prime.
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+10
1
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3, 6, 9, 12, 13, 14, 15, 18, 20, 21, 24, 25, 27, 30, 32, 33, 34, 36, 39, 40, 41, 42, 45, 47, 48, 49, 51, 53, 54, 55, 57, 58, 60, 62, 63, 66, 69, 70, 71, 72, 75, 76, 78, 79, 80, 81, 83, 84, 87, 89, 90, 91, 92, 93, 94, 96, 97, 99, 100
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OFFSET
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1,1
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LINKS
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EXAMPLE
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Distribution of the terms in the following triangular array:
*;
*,*;
*,*,*;
*,*,6,*;
3,*,*,*,*;
*,*,*,*,14,*;
*,*,*,*,*,*,*;
*,*,*,15,*,*,*,*;
*,*,13,*,*,*,*,32,*;
6,*,*,*,*,27,*,*,*,*;
*,*,*,*,25,*,*,*,*,48,*; etc.
where * marks the non-integer values of (2*h*k + k + h - 1)/5 with n >= k >= 1. - Vincenzo Librandi, Jan 14 2013
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MATHEMATICA
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PROG
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(Magma) [n: n in [0..150] | not IsPrime(10*n + 3)]; // Vincenzo Librandi, Jan 14 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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A102915
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Numbers n such that n3 is prime and n is a multiple of 10.
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+10
0
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0, 10, 50, 110, 130, 200, 220, 250, 280, 290, 320, 380, 400, 460, 470, 490, 500, 530, 550, 590, 620, 670, 680, 710, 760, 770, 880, 910, 920, 940, 980, 1010, 1030, 1090, 1100, 1150, 1190, 1220, 1250, 1270, 1300, 1310, 1390, 1430, 1450, 1580, 1610, 1660, 1670, 1690, 1720, 1790, 1850, 1880
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OFFSET
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1,2
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LINKS
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EXAMPLE
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If t=10, then t3 = 103 (prime).
If t=280, then t3 = 2803 (prime).
If t=490, then t3 = 4903 (prime).
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MATHEMATICA
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Select[10*Range[0, 200], PrimeQ[10#+3]&] (* Harvey P. Dale, Mar 23 2015 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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A126332
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Numbers k such that 10k + 13 is prime.
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+10
0
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0, 1, 3, 4, 6, 7, 9, 10, 15, 16, 18, 21, 22, 25, 27, 28, 30, 34, 36, 37, 42, 43, 45, 49, 51, 55, 58, 60, 63, 64, 66, 67, 72, 73, 76, 81, 84, 85, 87, 94, 97, 100, 102, 105, 108, 109, 111, 114, 115, 118, 120, 121, 127, 129, 136, 141, 142, 144, 147, 148, 151, 153, 154, 157
(list;
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refs;
listen;
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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For k = 100, 10*k + 13 = 1013 (prime).
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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