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 1-8 of 8 results.

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

A038133 From a subtractive Goldbach conjecture: odd primes that are not cluster primes.

Original entry on oeis.org

97, 127, 149, 191, 211, 223, 227, 229, 251, 257, 263, 269, 293, 307, 331, 337, 347, 349, 367, 373, 379, 383, 397, 409, 419, 431, 457, 479, 487, 499, 521, 541, 547, 557, 563, 569, 587, 593, 599, 631, 641, 673, 691, 701, 709, 719, 727, 733, 739, 743, 751
Offset: 1

Views

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. Sequence gives primes not having this property.

References

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

Links

Crossrefs

Cf. A038134, 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, j0, AppendTo[lst, p[[i]]]]]; lst

Extensions

More terms from Christian G. Bower, Feb 15 1999

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

A121044 Greatest cluster prime less than 10^n.

Original entry on oeis.org

7, 89, 983, 9931, 99991, 999331, 9997879, 99999551, 999998693, 9999995363, 99999976319, 999999998533, 9999999954787
Offset: 1

Views

Author

T. D. Noe, Jul 21 2006

Keywords

Comments

These numbers are useful for generating intermediate cluster primes because the best algorithm for generating cluster primes requires starting with a known cluster prime.

Links

Crossrefs

Cf. A038134 (cluster primes), A039506 (number of cluster primes < 10^n), A121045.

A121045 Least cluster prime greater than 10^n.

Original entry on oeis.org

3, 11, 101, 1013, 10141, 100153, 1000193, 10000763, 100000673, 1000000933, 10000002713, 100000005041, 1000000010489, 10000000003243
Offset: 0

Views

Author

T. D. Noe, Jul 21 2006

Keywords

Comments

These numbers are useful for generating intermediate cluster primes because the best algorithm for generating cluster primes requires starting with a known cluster prime.

Links

Crossrefs

Cf. A038134 (cluster primes), A039506 (number of cluster primes < 10^n), A121044.

A120935 Largest prime in the cluster of n primes whose first prime is given in A120934.

Original entry on oeis.org

2, 13, 463, 3259, 165713, 10526573, 495233371, 196039655899, 10687033762063, 79006533276973, 4313367040646779, 1740318019946551973
Offset: 1

Views

Author

T. D. Noe, Jul 21 2006

Keywords

Comments

For n>1, it appears that each prime is a cluster prime. See A038134.

Crossrefs

Cf. A020497.

Formula

a(n)= A120934(n)+A008407(n)

Extensions

a(12) from Donovan Johnson, Apr 18 2012

A137467 a(n) = i + j - k, where n = p(i) + p(j) - p(k), such that p(i), p(j), and p(k) are distinct primes, i + j - k = minimum, and n >= 3.

Original entry on oeis.org

1, 2, 3, 2, 3, 3, 4
Offset: 3

Views

Author

Ctibor O. Zizka, Apr 19 2008

Keywords

Comments

Is it true for all n : n = p(i) + p(j) - p(k)?

Examples

			For n = 6, 6 = p(1) + p(5) - p(4) = 2 + 11 - 7; so a(6) = 1 + 5 - 4 = 2.

Crossrefs

Cf. A000040, A038134.
Showing 1-8 of 8 results.

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

Content is available under The OEIS End-User License Agreement.