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.

A089524 A089492 indexed by A000040.

Original entry on oeis.org

117814, 303839, 588398, 641658, 667591, 718808, 755409, 940389, 1168122, 1198507, 1229482, 1229483, 1588488, 1698574, 1764688, 1840175, 1933195, 1936524, 2249818, 2849725, 2859255, 3307463, 3363452, 3414415, 3481752
Offset: 1

Views

Author

Ray Chandler, Nov 07 2003

Keywords

Examples

			p(62178)=776117, 2*776117 + 3 = 1552237 = p(117814);
p(62179)=776119, 2*776119 + 3 = 1552241 = p(117815);
p(62180)=776137, 2*776137 + 3 = 1552277 = p(117816);
p(62181)=776143, 2*776143 + 3 = 1552289 = p(117817).

Crossrefs

Subsequence of A089525.
Cf. A089007, A089009, A089492.

Formula

a(n) = k such that A089492(n) = A000040(k).
a(n) = A000720(A089492(n)). - Michel Marcus, Aug 06 2021

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

A089009 Numbers n such that 2*p(n)+3, 2*p(n+1)+3, 2*p(n+2)+3, 2*p(n+3)+3 are consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

62178, 159794, 308508, 336390, 350046, 376777, 395837, 492449, 611190, 627072, 643266, 643267, 830501, 887720, 922151, 961608, 1009939, 1011676, 1174998, 1487107, 1492042, 1725364, 1754501, 1780962, 1815913, 2048082, 2235662
Offset: 1

Views

Author

Pierre CAMI, Nov 03 2003

Keywords

Examples

			p(62178)=776117, 2*776117+3=1552237=p(117814).
p(62179)=776119, 2*776119+3=1552241=p(117815).
p(62180)=776137, 2*776137+3=1552277=p(117816).
p(62181)=776143, 2*776143+3=1552289=p(117817).

Links

Crossrefs

Subsequence of A088066.
Cf. A089007, A089492, A089524.

Programs

  • Mathematica
    cpQ[n_]:=Module[{p1=2Prime[n]+3,p2=2Prime[n+1]+3,p3=2Prime[n+2]+3,p4 = 2Prime[ n+3]+3}, PrimeQ[ p1] &&NextPrime[p1]==p2&&NextPrime[p2]==p3 && NextPrime[p3]==p4]; Select[Range[2236000],cpQ] (* Harvey P. Dale, Aug 15 2020 *)

Extensions

Corrected and extended by Ray Chandler, Nov 04 2003

A089007 Sequence of primes p(n) such that 2*p(n)+3, 2*p(n+1)+3, 2*p(n+2)+3, 2*p(n+3)+3 are four consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

776117, 2157733, 4387067, 4814597, 5024039, 5437573, 5734693, 7249369, 9140429, 9394813, 9654977, 9654989, 12693013, 13632727, 14199319, 14848513, 15649133, 15677647, 18396449, 23659483, 23743943, 27724843, 28224293, 28677529
Offset: 1

Views

Author

Pierre CAMI, Nov 03 2003

Keywords

Examples

			776117 is in the sequence because it is the 62178th prime, followed by the primes 776119, 776137 and 776143; and 2*776117+3 = 1552237, 2*776119+3 = 1552241, 2*776137+3 = 1552277 and 2*776143+3 = 1552289 which are the 117814th, 117815th, 117816th and 117817th prime respectively.

Crossrefs

Subsequence of A088119.
For values of n see A089009: a(n) = A000040(A089009(n)).
Cf. A089492, A089524.

Programs

  • Mathematica
    lst = {}; Do[ If[ PrimeQ[2Prime[n] + 3], If[ PrimeQ[2Prime[n + 1] + 3], If[ PrimeQ[2Prime[n + 2] + 3], If[ PrimeQ[2Prime[n + 3] + 3], If[ PrimePi[2Prime[n] + 3] + 3 == PrimePi[2Prime[n + 3] + 3], AppendTo[lst, Prime[n]]] ]]]], {n, 2048081}] (* Robert G. Wilson v, Jan 13 2005 *)

Extensions

Corrected and extended by Ray Chandler, Nov 04 2003
Entry revised by N. J. A. Sloane, Apr 01 2006
Showing 1-3 of 3 results.

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

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