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Search: a102338 -id:a102338
Displaying 1-8 of 8 results found. page 1
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A007811 Numbers k for which 10k+1, 10k+3, 10k+7 and 10k+9 are primes. +10
51
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 3*A014561(n) + 1. - Zak Seidov, Sep 21 2009
MAPLE
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
MATHEMATICA
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 *)
PROG
(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]
-- Reinhard Zumkeller, Jul 18 2014
(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
CROSSREFS
Cf. A024912, A102338, A102342, A102700, A007530, A014561, A008471, A032352, A216292, A216293, A125855.
Cf. A010051, A245304, A245305.
KEYWORD
nonn
AUTHOR
N. J. A. Sloane and J. H. Conway, Mar 15 1996
STATUS
approved
A030431 Primes of form 10n+3. +10
48
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also primes of form 5n+3.
Union of A132233, A132235, {3}. - Ray Chandler, Apr 07 2009
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
5 is not quadratic residue of primes of this form. - Vincenzo Librandi, Jun 25 2014
Intersection of A000040 and A017305. - Iain Fox, Dec 30 2017
LINKS
Michael B. Porter, Table of n, a(n) for n = 1..100000
A. Granville and G. Martin, Prime number races, arXiv:math/0408319 [math.NT], 2004.
FORMULA
a(n) = 10*A102338(n) + 3.
MATHEMATICA
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 *)
PROG
(PARI) select(n->n%10==3, primes(500)) \\ Charles R Greathouse IV, Apr 29 2015
CROSSREFS
Cf. A045414, A049508, A053179, A102338.
KEYWORD
nonn
AUTHOR
Warut Roonguthai
EXTENSIONS
Extended by Ray Chandler, Nov 07 2006
STATUS
approved
A023238 Primes p such that 10*p + 3 is also prime. +10
7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
John Cerkan, Table of n, a(n) for n = 1..10000
MAPLE
A023238:=n->`if`(isprime(n) and isprime(10*n+3), n, NULL): seq(A023238(n), n=1..10^3); # Wesley Ivan Hurt, Sep 08 2016
MATHEMATICA
Select[Prime[Range[200]], PrimeQ[10# + 3] &] (* Alonso del Arte, Jun 24 2014 *)
PROG
(Magma) [n: n in [0..1000] | IsPrime(n) and IsPrime(10*n+3)] // Vincenzo Librandi, Nov 20 2010
CROSSREFS
Cf. A023239.
Subsequence of A102338.
KEYWORD
nonn
AUTHOR
David W. Wilson
STATUS
approved
A049508 Numbers k such that prime(k) == 3 (mod 10). +10
7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 1/4 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021
LINKS
Table of n, a(n) for n=1..59.
FORMULA
a(n) = A000720(A030431(n)). - Ray Chandler, Nov 07 2006
MATHEMATICA
Select[Range[240], Mod[Prime[ # ], 10] == 3 &] (* Ray Chandler, Nov 07 2006 *)
CROSSREFS
Cf. A000720, A030431, A102338.
Cf. A049509, A049510, A049511.
KEYWORD
easy,nonn
AUTHOR
J. Lowell
EXTENSIONS
Edited and extended by Ray Chandler, Nov 07 2006
STATUS
approved
A023269 Primes that remain prime through 2 iterations of function f(x) = 10x + 3. +10
1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Primes p such that 10*p+3 and 100*p+33 are also primes. - Vincenzo Librandi, Aug 04 2010
LINKS
John Cerkan, Table of n, a(n) for n = 1..10000
MATHEMATICA
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 *)
PROG
(Magma) [n: n in [1..100000] | IsPrime(n) and IsPrime(10*n+3) and IsPrime(100*n+33)] // Vincenzo Librandi, Aug 04 2010
CROSSREFS
Subsequence of A023238 and of A102338.
KEYWORD
nonn
AUTHOR
David W. Wilson
STATUS
approved
A153403 Numbers n such that 10*n+3 is not prime. +10
1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
EXAMPLE
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
MATHEMATICA
lst={}; Do[p=10*n+3; If[ !PrimeQ[p], AppendTo[lst, n]], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 12 2010 *)
PROG
(Magma) [n: n in [0..150] | not IsPrime(10*n + 3)]; // Vincenzo Librandi, Jan 14 2013
CROSSREFS
Cf. A102338.
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Dec 25 2008
STATUS
approved
A102915 Numbers n such that n3 is prime and n is a multiple of 10. +10
0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..54.
EXAMPLE
If t=10, then t3 = 103 (prime).
If t=280, then t3 = 2803 (prime).
If t=490, then t3 = 4903 (prime).
MATHEMATICA
Select[10*Range[0, 200], PrimeQ[10#+3]&] (* Harvey P. Dale, Mar 23 2015 *)
CROSSREFS
Cf. A102338.
KEYWORD
base,nonn
AUTHOR
Parthasarathy Nambi, Mar 01 2005
STATUS
approved
A126332 Numbers k such that 10k + 13 is prime. +10
0
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; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Table of n, a(n) for n=1..64.
FORMULA
a(k) = A102338(k+1) - 1. - R. J. Mathar, Jul 08 2009
EXAMPLE
For k = 100, 10*k + 13 = 1013 (prime).
PROG
(Magma) [n: n in [0..1000] | IsPrime(10*n + 13)] // Vincenzo Librandi, Nov 23 2010
(PARI) is(n)=isprime(10*n+13) \\ Charles R Greathouse IV, Jun 13 2017
CROSSREFS
Cf. A102342, A126785.
KEYWORD
nonn,easy
AUTHOR
Parthasarathy Nambi, Mar 10 2007
STATUS
approved
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Last modified August 29 23:09 EDT 2024. Contains 375519 sequences. (Running on oeis4.)