cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A137177 Where records occur in A096915.

Original entry on oeis.org

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
Offset: 1

Views

Author

M. F. Hasler, Jan 13 2009

Keywords

Crossrefs

Cf. A096915, A144593.

Extensions

a(26)-a(35) from Donovan Johnson, Jul 10 2011

A144593 Records in A096915.

Original entry on oeis.org

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
Offset: 1

Views

Author

M. F. Hasler, Jan 13 2009

Keywords

Crossrefs

Cf. A096915, A137177.

Extensions

a(26)-a(35) from Donovan Johnson, Jul 10 2011

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.

Original entry on oeis.org

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
Offset: 1

Views

Author

Amarnath Murthy, Oct 15 2003

Keywords

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

Crossrefs

Cf. A096915, A065112.

Programs

  • 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

Extensions

More terms from Ray Chandler, Oct 18 2003

A089777 a(n) = smallest prime of the form n followed by a prime.

Original entry on oeis.org

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
Offset: 1

Views

Author

Amarnath Murthy, Nov 24 2003

Keywords

Comments

Open problem(?): show that a(n) always exists.

Links

Crossrefs

Cf. A096915 (gives the primes that are appended to n). - R. J. Mathar, Jan 05 2009

Programs

  • 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 *)

Extensions

Extended by T. D. Noe and R. J. Mathar, Jan 06 2009

A103835 Smallest prime p, larger than previous term, such that concatenation of n and p is a prime.

Original entry on oeis.org

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
Offset: 1

Views

Author

Zak Seidov, Mar 30 2005

Keywords

Comments

Cf. A096915.

Examples

			a(10)=97 because 1097 is prime, while 1071,1073,1079,1083,1089 are all composite.

Crossrefs

Cf. A096915, A103836.

Programs

  • 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

A103836 Smallest palindromic prime p, larger than previous term, such that concatenation of n and p is a prime.

Original entry on oeis.org

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
Offset: 1

Views

Author

Zak Seidov, Mar 30 2005

Keywords

Comments

Cf. A096915

Examples

			a(4) = 373 because 4373 is prime, while 4191, 4313, 4353 are all composite.

Crossrefs

Cf. A096915, A103835.
Subsequence of A002385.

Programs

  • 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

A131757 Period 10: repeat 3, 3, 3, -7, 3, 3, -7, 3, 3, -7.

Original entry on oeis.org

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
Offset: 0

Views

Author

Paul Curtz, Oct 04 2007

Keywords

Links

Crossrefs

Cf. A010705, A096915.

Programs

Showing 1-7 of 7 results.

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