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.

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

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

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

A089529 A089528 indexed by A000040.

Original entry on oeis.org

6, 12, 24, 59, 77, 78, 87, 88, 126, 135, 158, 312, 331, 379, 415, 445, 455, 456, 824, 924, 955, 971, 1069, 1080, 1148, 1226, 1368, 1402, 1480, 1592, 1597, 1826, 1934, 2002, 2014, 2035, 2093, 2187, 2212, 2254, 2315, 2353, 2461, 2587, 2619, 2653, 2766, 2792
Offset: 1

Views

Author

Ray Chandler, Nov 07 2003

Keywords

Examples

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

Crossrefs

Subsequence of A089532.
Cf. A089526, A089527, A089528.

Formula

a(n) = k such that A089528(n) = A000040(k).
a(n) = A000720(A089528(n)). - Michel Marcus, Aug 04 2021

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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