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.

A088066 Numbers n such that 2*p(n)+3, 2*p(n+1)+3, 2*p(n+2)+3 are consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

44, 48, 253, 1834, 4193, 6380, 6532, 6788, 7187, 8216, 8711, 9318, 9519, 9817, 9908, 10947, 11971, 13308, 13880, 17326, 18366, 22664, 27938, 29576, 31931, 34773, 35960, 40853, 45454, 48736, 52256, 52586, 53010, 53956, 54758, 59618, 62178
Offset: 1

Views

Author

Pierre CAMI, Nov 02 2003

Keywords

Examples

			p(44)=193, 2*193+3=389=p(77)
p(45)=197, 2*197+3=397=p(78)
p(46)=199, 2*199+3=401=p(79)

Crossrefs

Subsequence of A089526.
Cf. A088119, A089450, A089525.

Extensions

More terms from Ray Chandler, Nov 03 2003

A089450 Sequence of primes 2*p(k) + 3 such that 2*p(k) + 3, 2*p(k+1) + 3, 2*p(k+2) + 3 are consecutive primes, where p(i) denotes the i-th prime. Sequence terms are 2*p(k) + 3.

Original entry on oeis.org

389, 449, 3217, 31469, 79757, 127297, 130817, 136417, 145349, 168601, 179957, 193577, 198277, 205069, 207377, 231677, 255617, 287137, 300749, 384001, 409589, 515737, 648437, 689917, 750509, 824069, 854869, 982301, 1103437, 1190237
Offset: 1

Views

Author

Ray Chandler, Nov 03 2003

Keywords

Examples

			p(44)=193, 2*193 + 3 = 389 = p(77);
p(45)=197, 2*197 + 3 = 397 = p(78);
p(46)=199, 2*199 + 3 = 401 = p(79).

Crossrefs

Subsequence of A089528.
Cf. A088066, A088119, A089525.

Programs

  • Mathematica
    cpQ[n_]:=Module[{p1=2n+3,p2=2NextPrime[n]+3,p3=2NextPrime[n,2]+3,pr = PrimePi[ 2n+3]},{p1,p2,p3}==Prime[Range[pr,pr+2]]]; 2#+3&/@ Select[ Prime[ Range[50000]],cpQ] (* Harvey P. Dale, Sep 24 2019 *)

Formula

a(n) = 2*A088119(n) + 3 = 2*A000040(A088066(n)) + 3 = A000040(A089525(n)).

Extensions

Definition clarified by Harvey P. Dale, Sep 24 2019
Offset changed to 1 by Jinyuan Wang, Aug 04 2021

A089525 A089450 indexed by A000040.

Original entry on oeis.org

77, 87, 455, 3386, 7811, 11926, 12233, 12705, 13448, 15382, 16338, 17462, 17844, 18387, 18580, 20577, 22492, 25001, 26060, 32604, 34578, 42718, 52713, 55807, 60272, 65730, 67963, 77232, 85964, 92239, 98963, 99587, 100386, 102163, 103689
Offset: 1

Views

Author

Ray Chandler, Nov 07 2003

Keywords

Examples

			prime(44)=193, 2*193 + 3 = 389 = prime(77);
prime(45)=197, 2*197 + 3 = 397 = prime(78);
prime(46)=199, 2*199 + 3 = 401 = prime(79).

Crossrefs

Subsequence of A089529.
Cf. A088066, A088119, A089450.

Formula

a(n) = k such that A089450(n) = A000040(k).
a(n) = A000720(A089450(n)). - Michel Marcus, Aug 04 2021

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 04 2021

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 1-4 of 4 results.

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

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