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.

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).
		

Crossrefs

Subsequence of A088066.

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

A089492 Sequence of primes 2*p(k) + 3 such that 2*p(k) + 3, 2*p(k+1) + 3, 2*p(k+2) + 3, 2*p(k+3) + 3 are consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

1552237, 4315469, 8774137, 9629197, 10048081, 10875149, 11469389, 14498741, 18280861, 18789629, 19309957, 19309981, 25386029, 27265457, 28398641, 29697029, 31298269, 31355297, 36792901, 47318969, 47487889, 55449689
Offset: 1

Views

Author

Ray Chandler, Nov 04 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 A089450.

Programs

  • PARI
    a089492(limit)={my(pv=[2,3,5,0],v3=[3,3,3,3],ks(k)=2*k+3);forprime(p=7,limit,pv[4]=p;if(vecsum(isprime(2*pv+v3))==4&&primepi(ks(pv[4]))-primepi(ks(pv[1]))==3,print1(ks(pv[1]),", "));pv[1]=pv[2];pv[2]=pv[3];pv[3]=pv[4])};
    a089492(30000000) \\ Hugo Pfoertner, Aug 06 2021

Formula

a(n) = 2*A089007(n) + 3 = 2*A000040(A089009(n)) + 3 = A000040(A089524(n)).

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

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.

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
Showing 1-3 of 3 results.