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Search: a096915 -id:a096915
Displaying 1-7 of 7 results found. page 1
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A137177 Where records occur in A096915. +20
2
1, 3, 14, 71, 76, 131, 188, 196, 232, 314, 535, 695, 1451, 2474, 3868, 7717, 41284, 52462, 90760, 119008, 264433, 487534, 618691, 935477, 959456, 3232220, 5149055, 6734713, 24668330, 92436217, 144794399, 603533275, 927592756, 969468212, 1182908572 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..35.
CROSSREFS
Cf. A096915, A144593.
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jan 13 2009
EXTENSIONS
a(26)-a(35) from Donovan Johnson, Jul 10 2011
STATUS
approved
A144593 Records in A096915. +20
2
3, 7, 23, 29, 43, 47, 59, 61, 79, 89, 97, 131, 179, 239, 283, 313, 367, 373, 379, 541, 577, 601, 607, 617, 857, 911, 953, 1063, 1301, 1321, 1499, 1783, 1867, 1913, 1933 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..35.
CROSSREFS
Cf. A096915, A137177.
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jan 13 2009
EXTENSIONS
a(26)-a(35) from Donovan Johnson, Jul 10 2011
STATUS
approved
A088606 Smallest number k such that concatenation of k and prime(n) is a prime, or 0 if no other number exists. a(1) = a(3) = 0. +10
3
0, 1, 0, 1, 2, 1, 3, 4, 2, 2, 1, 1, 2, 4, 3, 3, 3, 4, 1, 2, 1, 1, 2, 3, 1, 5, 1, 5, 1, 2, 4, 2, 2, 4, 11, 1, 4, 1, 3, 6, 2, 1, 3, 1, 5, 6, 4, 1, 5, 1, 5, 2, 4, 2, 3, 6, 2, 3, 1, 2, 1, 2, 1, 2, 3, 6, 3, 4, 2, 4, 6, 3, 1, 1, 6, 2, 2, 4, 12, 1, 5, 4, 5, 1, 1, 5, 3, 3, 3, 3, 2, 5, 1, 3, 1, 2, 17, 2, 1, 3, 3, 2, 5, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Subsidiary sequences: (set(1)) Index of the start of the first occurrence of a string of n consecutive 1's or 2's or 3's etc. (set (2)): a(n) = smallest prime such that concatenation of 1 with n successive primes starting from a(n) gives primes in each case. (n primes are obtained.) Similarly for 2, 3, etc. Conjecture: The subsidiary sequences are infinite.
A065112(n) = a(n) concatenated with prime(n). - Bill McEachen, May 27 2021
LINKS
Table of n, a(n) for n=1..104.
PROG
(PARI) a(n) = if ((n==1) || (n==3), 0, my(k=1); while (!isprime(eval(Str(k, prime(n)))), k++); k); \\ Michel Marcus, Jul 11 2021
CROSSREFS
Cf. A096915, A065112.
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Oct 15 2003
EXTENSIONS
More terms from Ray Chandler, Oct 18 2003
STATUS
approved
A089777 a(n) = smallest prime of the form n followed by a prime. +10
2
13, 23, 37, 43, 53, 67, 73, 83, 97, 103, 113, 127, 137, 1423, 157, 163, 173, 1811, 193, 2011, 2111, 223, 233, 2411, 257, 263, 277, 283, 293, 307, 313, 3217, 337, 347, 353, 367, 373, 383, 397, 4013, 4111, 4211, 433, 443, 457, 463, 4723, 487, 4919, 503, 5113 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Open problem(?): show that a(n) always exists.
LINKS
T. D. Noe, Table of n, a(n) for n=1..10000
MAPLE
cat2 := proc(a, b) local dgs ; dgs := max(1, ilog10(b)+1) ; a*10^dgs+b ; end: A089777 := proc(k) local i, p, q ; for i from 1 do p := ithprime(i) ; q := cat2(k, p) ; if isprime(q) then RETURN(q) ; fi; od: end: for k from 1 to 80 do printf("%d, ", A089777(k)) ; od: # R. J. Mathar, Jan 05 2009
MATHEMATICA
Table[k=2; While[p=FromDigits[Join[IntegerDigits[n], IntegerDigits[Prime[k]]]]; !PrimeQ[p], k++ ]; p, {n, 100}] (* T. D. Noe, Jan 06 2009 *)
CROSSREFS
Cf. A096915 (gives the primes that are appended to n). - R. J. Mathar, Jan 05 2009
KEYWORD
base,easy,nonn
AUTHOR
Amarnath Murthy, Nov 24 2003
EXTENSIONS
Extended by T. D. Noe and R. J. Mathar, Jan 06 2009
STATUS
approved
A103835 Smallest prime p, larger than previous term, such that concatenation of n and p is a prime. +10
1
3, 11, 13, 19, 23, 31, 43, 53, 67, 97, 113, 149, 151, 173, 193, 223, 239, 251, 373, 389, 397, 409, 431, 439, 457, 479, 487, 499, 569, 577, 601, 647, 739, 757, 797, 809, 811, 821, 827, 829, 863, 929, 991, 1109, 1181, 1297, 1301, 1303, 1327, 1367, 1409, 1429 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Cf. A096915.
LINKS
Table of n, a(n) for n=1..52.
EXAMPLE
a(10)=97 because 1097 is prime, while 1071,1073,1079,1083,1089 are all composite.
PROG
(Python)
from sympy import isprime, nextprime
def ispal(n): s = str(n); return s == s[::-1]
def aupto(lim):
n, p, alst = 1, 2, []
while p <= lim:
if isprime(int(str(n)+str(p))): n, alst = n + 1, alst + [p]
p = nextprime(p)
return alst
print(aupto(1429)) # Michael S. Branicky, Mar 11 2021
CROSSREFS
Cf. A096915, A103836.
KEYWORD
nonn,base
AUTHOR
Zak Seidov, Mar 30 2005
STATUS
approved
A103836 Smallest palindromic prime p, larger than previous term, such that concatenation of n and p is a prime. +10
1
3, 11, 181, 373, 12821, 14741, 32323, 72227, 74747, 77977, 78887, 79997, 90709, 94049, 94849, 98689, 1055501, 1065601, 1114111, 1129211, 1134311, 1177711, 1180811, 1186811, 1190911, 1262621, 1333331, 1338331, 1407041, 1409041, 1411141, 1461641, 1463641 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Cf. A096915
LINKS
Table of n, a(n) for n=1..33.
EXAMPLE
a(4) = 373 because 4373 is prime, while 4191, 4313, 4353 are all composite.
PROG
(Python)
from sympy import isprime, nextprime
def ispal(n): s = str(n); return s == s[::-1]
def aupto(lim):
n, p, alst = 1, 2, []
while p <= lim:
if ispal(p) and isprime(int(str(n)+str(p))): n, alst = n + 1, alst + [p]
p = nextprime(p)
return alst
print(aupto(1463641)) # Michael S. Branicky, Mar 11 2021
CROSSREFS
Cf. A096915, A103835.
Subsequence of A002385.
KEYWORD
nonn,base
AUTHOR
Zak Seidov, Mar 30 2005
STATUS
approved
A131757 Period 10: repeat 3, 3, 3, -7, 3, 3, -7, 3, 3, -7. +10
0
3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3, 3, 3, -7, 3, 3, -7, 3, 3, -7, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Table of n, a(n) for n=0..110.
Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1,-1,-1,-1,-1,-1).
MATHEMATICA
PadRight[{}, 120, {3, 3, 3, -7, 3, 3, -7, 3, 3, -7}] (* Harvey P. Dale, Aug 07 2018 *)
PROG
(PARI) a(n)=[3, 3, 3, -7, 3, 3, -7, 3, 3, -7][n%10+1] \\ Charles R Greathouse IV, Jul 13 2016
CROSSREFS
Cf. A010705, A096915.
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Oct 04 2007
STATUS
approved
page 1

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Last modified August 30 13:06 EDT 2024. Contains 375543 sequences. (Running on oeis4.)