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 1-2 of 2 results.

A115095 Positions of 4's in A038800 with offset 1.

Original entry on oeis.org

1, 2, 11, 20, 83, 149, 188, 209, 326, 347, 566, 944, 1301, 1565, 1574, 1607, 1805, 1892, 1943, 2102, 2228, 2531, 3173, 3485, 4379, 5135, 5534, 6299, 6722, 6950, 7223, 7727, 7970, 8105, 8273, 8882, 9785, 9914, 10112, 10985, 11654, 11930, 12221, 13547
Offset: 1

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Author

Zak Seidov, Mar 01 2006

Keywords

Comments

Starting with a(2)=2, numbers m such that 10*(m-1)+{1,3,7,9} are all primes.
Essentially the same as A064975. - R. J. Mathar, Aug 11 2008

Examples

			11 is a term because 10*(11-1)+{1,3,7,9} = 101,103,107,109 are all prime.

References

  • 4 is the maximum possible number of primes between 10*n and 10*(n+1).

Links

Crossrefs

Cf. A064975 (essentially the same).
Cf. A038800 (number of primes between 10*n and 10*n+9).
Cf. A007811.

Programs

  • Mathematica
    Join[{1}, Select[Range[2, 15000, 3], AllTrue[10*# - {1, 3, 7, 9}, PrimeQ] &]] (* Paolo Xausa, Jul 15 2025 *)

Formula

a(1) = 1; for n >= 2, a(n) = A007811(n-1) + 1. - Paolo Xausa, Jul 15 2025

Extensions

Name edited by Paolo Xausa, Jul 20 2025

A243408 Primes p such that 10*p-1, 10*p-3, 10*p-7 and 10*p-9 are all prime.

Original entry on oeis.org

2, 11, 83, 149, 347, 1301, 1607, 2531, 6299, 7727, 8273, 17117, 20183, 21737, 24371, 26669, 39227, 40277, 53951, 54917, 63347, 66359, 66467, 73637, 82217, 82373, 101537, 102251, 106397, 106871, 117203, 132971, 134033, 135221, 140237, 144701, 146141, 151433, 152597
Offset: 1

Views

Author

Derek Orr, Jun 04 2014

Keywords

Comments

This is a subsequence of A064975.

Examples

			2 is prime, 10*2-1 = 19 is prime, 10*2-3 = 17 is prime, 10*2-7 = 13 is prime, 10*2-9 = 11 is prime. Thus 2 is a member of this sequence.

Links

Crossrefs

Cf. A067267, A064975.

Programs

  • Mathematica
    Select[ Range@ 153000,PrimeQ[#] && PrimeQ[10#-1] && PrimeQ[10#-3] && PrimeQ[10#-7] && PrimeQ[10#-9] &] (* Robert G. Wilson v, Jun 06 2014 *)
Select[Prime[Range[15000]],AllTrue[10#-{1,3,7,9},PrimeQ]&] (* Harvey P. Dale, Aug 18 2024 *)
  • PARI
    for(n=1,10^5,if(ispseudoprime(10*prime(n)-1) && ispseudoprime(10*prime(n)-3) && ispseudoprime(10*prime(n)-7) && ispseudoprime(10*prime(n)-9),print1(prime(n),", ")))
  • Python
    import sympy
from sympy import isprime
from sympy import prime
{print(prime(n),end=', ') for n in range(1,10**5) if isprime(10*prime(n)-1) and isprime(10*prime(n)-3) and isprime(10*prime(n)-7) and isprime(10*prime(n)-9)}
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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