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.

A089526 Numbers n such that 2*p(n)+3 and 2*p(n+1)+3 are consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

3, 7, 14, 33, 44, 45, 48, 49, 70, 75, 90, 174, 186, 213, 225, 246, 253, 254, 447, 505, 524, 531, 589, 592, 625, 665, 745, 766, 806, 866, 868, 989, 1047, 1084, 1091, 1105, 1131, 1191, 1202, 1228, 1257, 1280, 1333, 1395, 1410, 1429, 1495, 1512, 1550, 1643, 1651
Offset: 1

Views

Author

Ray Chandler, Nov 07 2003

Keywords

Examples

			p(3)=5, 2*5+3=13=p(6)
p(4)=7, 2*7+3=17=p(7)

Links

Crossrefs

Subsequence of A089530. Cf. A089527, A089528, A089529.

Programs

  • Mathematica
    cpQ[n_]:=Module[{p=2Prime[n]+3},PrimeQ[p]&&NextPrime[p]==2Prime[n+1]+3]; Select[Range[1700],cpQ] (* Harvey P. Dale, Nov 29 2014 *)

A089528 Primes p of the form 2*prime(k) + 3 such that 2*prime(k+1) + 3 is the next prime after p.

Original entry on oeis.org

13, 37, 89, 277, 389, 397, 449, 457, 701, 761, 929, 2069, 2221, 2609, 2857, 3121, 3217, 3221, 6329, 7229, 7537, 7649, 8581, 8677, 9277, 9941, 11317, 11681, 12401, 13421, 13469, 15649, 16729, 17401, 17497, 17729, 18257, 19289, 19489, 19937, 20509
Offset: 1

Views

Author

Ray Chandler, Nov 07 2003

Keywords

Examples

			p(3)=5, 2*5 + 3 = 13 = p(6);
p(4)=7, 2*7 + 3 = 17 = p(7).

Links

Crossrefs

Subsequence of A089531.
Cf. A089526, A089527, A089529.

Programs

  • Mathematica
    Select[Partition[2#+3&/@Prime[Range[2500]],2,1],AllTrue[#,PrimeQ] && NextPrime[ #[[1]]]==#[[2]]&][[All,1]] (* Harvey P. Dale, Dec 14 2021 *)
  • PARI
    forprime(p=2,10500,my(p23=2*p+3);if(isprime(p23),my(pp=2*nextprime(p+1)+3);if(isprime(pp)&&pp==nextprime(p23+1),print1(p23,", ")))) \\ Hugo Pfoertner, Aug 04 2021

Formula

a(n) = 2*A089527(n) + 3 = 2*A000040(A089526(n)) + 3 = A000040(A089529(n)).

Extensions

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

A089527 p(k) such that 2*p(k)+3 and 2*p(k+1) + 3 are consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

5, 17, 43, 137, 193, 197, 223, 227, 349, 379, 463, 1033, 1109, 1303, 1427, 1559, 1607, 1609, 3163, 3613, 3767, 3823, 4289, 4337, 4637, 4969, 5657, 5839, 6199, 6709, 6733, 7823, 8363, 8699, 8747, 8863, 9127, 9643, 9743, 9967, 10253, 10459, 10979, 11593
Offset: 1

Views

Author

Ray Chandler, Nov 07 2003

Keywords

Examples

			p(3)=5, 2*5 + 3 = 13 = p(6);
p(4)=7, 2*7 + 3 = 17 = p(7).

Crossrefs

Subsequence of A023204.
Cf. A089526, A089528, A089529.

Formula

a(n) = A000040(A089526(n)).

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 04 2021
Showing 1-4 of 4 results.

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

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