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 1-3 of 3 results.

A233550 Gap g between 3 consecutive primes for the smallest k such that 6^n+k, 6^n+k+g, 6^n+k+2*g are consecutive primes in arithmetic progression.

Original entry on oeis.org

6, 6, 6, 6, 12, 6, 18, 12, 6, 24, 18, 12, 6, 18, 12, 42, 30, 12, 54, 24, 60, 30, 24, 36, 78, 18, 42, 132, 42, 24, 24, 60, 24, 72, 24, 36, 30, 6, 12, 30, 30, 120, 6, 36, 72, 30, 30, 18, 6, 60, 210, 66, 84, 30, 96, 24, 84, 6, 210, 78, 18, 228
Offset: 2

Views

Author

Pierre CAMI, Dec 16 2013

Keywords

Comments

Sequence starts for n=2 as no solution for n=1.
g is a multiple of 6 as otherwise 6^n+k, 6^n+k+g, or 6^n+k+2*g is divisible by 2 or 3. - Jonathan Sondow, Dec 16 2013

Examples

			6^2+11=47, 6^2+11+6=53, 6^2+11+2*6=59 are consecutive primes and k=11 is minimal, so a(2)=6. - _Jonathan Sondow_, Dec 16 2013

Links

Crossrefs

Cf. A233546 (associated k), A233742.

Programs

Formula

a(n) = 6*A233742(n). - Jonathan Sondow, Dec 16 2013

A233742 One sixth of gap g between 3 consecutive primes for the smallest k such that 6^n+k, 6^n+k+g, 6^n+k+2*g are consecutive primes in arithmetic progression.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 3, 2, 7, 5, 2, 9, 4, 10, 5, 4, 6, 13, 3, 7, 22, 7, 4, 4, 10, 4, 12, 4, 6, 5, 1, 2, 5, 5, 20, 1, 6, 12, 5, 5, 3, 1, 10, 35, 11, 14, 5, 16, 4, 14, 1, 35, 13, 3, 38
Offset: 2

Views

Author

Jonathan Sondow, Dec 16 2013

Keywords

Comments

g is a multiple of 6 as otherwise 6^n+k, 6^n+k+g, or 6^n+k+2*g is divisible by 2 or 3.
Sequence starts at n=2 as no solution for n=1.
k=A233546(n).

Crossrefs

Cf. A233546, A233550.

Formula

a(n) = A233550(n)/6.

A233823 Least prime in arithmetic progression of consecutive primes 6^n+k, 6^n+k+g, 6^n+k+2*g with smallest k.

Original entry on oeis.org

47, 251, 1361, 7817, 46877, 280591, 1680131, 10077959, 60470441, 362797949, 2176786421, 13060695047, 78364167257, 470184984721, 2821109908277, 16926659446819, 101559956670517, 609359740010929, 3656158440066719, 21936950640380099, 131621703842267647, 789730223053605439
Offset: 2

Views

Author

Jonathan Sondow, Dec 16 2013

Keywords

Comments

No solution for n = 1, so sequence starts at n = 2.
The primes are probable primes for n > 23.

Examples

			a(2) = 6^2 + A233546(2) = 36 + 11 = 47.

Crossrefs

Cf. A233546 (values of k), A233550 (values of g), A233742 (= g/6).

Formula

a(n) = 6^n + A233546(n).
Showing 1-3 of 3 results.

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

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