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 1-4 of 4 results.

A038134 From a subtractive Goldbach conjecture: cluster primes.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 101, 103, 107, 109, 113, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 193, 197, 199, 233, 239, 241, 271, 277, 281, 283, 311, 313, 317, 353, 359, 389, 401, 421, 433
Offset: 1

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Author

N. J. A. Sloane

Keywords

Comments

Erdős asks if there are infinitely many primes p such that every even number <= p-3 can be expressed as the difference between two primes each <= p.

References

  • R. K. Guy, Unsolved Problems In Number Theory, section C1.

Links

Crossrefs

Cf. A038133, A039506, A039507, A072325.

Programs

  • Mathematica
    m=1000; lst={}; n=PrimePi[m]-1; p=Table[Prime[i+1], {i, n}]; d=Table[0, {m/2}]; For[i=2, i<=n, i++, For[j=1, j

Extensions

More terms from Christian G. Bower, Feb 15 1999

A039506 Number of cluster primes less than 10^n.

Original entry on oeis.org

3, 23, 99, 420, 1807, 8287, 40017, 202208, 1059807, 5736717, 31911465, 182019293, 1060723057
Offset: 1

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Comments

The Blecksmith paper gives incorrect values of a(n) for n>8. - T. D. Noe, Jul 21 2006

Links

Crossrefs

Cf. A038133, A038134, A039507.
Cf. A121044, A121045 (cluster primes near 10^n).

Extensions

Corrected by T. D. Noe, Jul 21 2006

A039507 Number of odd non-cluster primes less than 10^n.

Original entry on oeis.org

0, 1, 68, 808, 7784, 70210, 624561, 5559246, 49787726, 449315793, 4086143347, 37425892724, 345004813781
Offset: 1

Views

Author

Christian G. Bower, Feb 15 1999

Keywords

Comments

The Blecksmith paper gives incorrect values of a(n) for n>8. - T. D. Noe, Jul 21 2006

Links

Crossrefs

Cf. A038133, A038134, A039506.

Formula

a(n) = A006880(n) - A039506(n) - 1. - T. D. Noe, Jul 21 2006

Extensions

Corrected by T. D. Noe, Jul 21 2006

A072325 Number of even numbers that cannot be expressed as the difference p-q of two odd primes q < p <= prime(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0
Offset: 2

Views

Author

T. D. Noe, Jul 15 2002, Nov 19 2006

Keywords

Comments

If a(n)=0, then Prime[n], called a cluster prime, is in A038134. If a(n)>0 then Prime[n] is in A038133.

Examples

			a(25)=1 because Prime[25]=97 and there is 1 even number, 88, that cannot be written as the difference of two odd primes less than or equal to 97.

Links

Crossrefs

Cf. A038133, A038134.

Programs

  • Mathematica
    m=10000; n=PrimePi[m]-1; p=Table[Prime[i+1], {i, n}]; d=Table[0, {m/2}]; c=Table[0, {n}]; For[i=2, i<=n, i++, For[j=1, j
Showing 1-4 of 4 results.

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

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