A182876 -id:A182876 - cp's OEIS frontend

A182873 First differences of the Ramanujan primes, A104272.

9, 6, 12, 12, 6, 12, 8, 4, 26, 4, 6, 20, 22, 2, 16, 12, 2, 46, 2, 4, 6, 2, 22, 6, 12, 26, 4, 36, 2, 18, 6, 28, 8, 10, 12, 2, 6, 22, 26, 4, 12, 66, 2, 16, 6, 6, 2, 6, 34, 2, 4, 6, 6, 18, 42, 8, 12, 12, 18, 40, 12, 2, 4, 26, 4, 24, 56, 4, 6, 20, 16, 26, 10, 2

Offset: 1

T. D. Noe, Dec 09 2010

nonn

That is, the gaps between adjacent Ramanujan primes.

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A182874, A182875, A182876, A182877.
Cf. A190874.
Cf. A001223 (differences between primes).

A182877 Record gaps between Ramanujan primes.

Original entry on oeis.org

9, 12, 26, 46, 66, 86, 90, 100, 114, 120, 126, 174, 190, 212, 280, 386, 396, 410, 480, 598, 726, 916, 964, 1000, 1074, 1090, 1218, 1280, 1378, 1380, 1614, 1728, 1774, 1924, 1998, 2378, 2452, 2514, 2608, 2852, 2866, 2870, 3080

Offset: 1

T. D. Noe, Dec 09 2010

nonn

The Ramanujan prime beginning the gap is in A182876.

Table of n, a(n) for n = 1..43

Cf. A005250 (increasing gaps between primes).

a(37)-a(43) from Dana Jacobsen, Apr 29 2015

A196673 Chebyshev primes that begin a record gap to the next Chebyshev prime.

Original entry on oeis.org

109, 113, 139, 317, 887, 1327, 1913, 3089, 8297, 11177, 29761, 45707, 113383, 164893, 291377, 401417, 638371, 1045841

Offset: 1

Michel Planat, Oct 05 2011

nonn

The Chebyshev primes (of index 1) are such odd primes that satisfy li[psi(p)]-li[psi(p-1)]<1 (sequence A196667), where li(x) is the logarithmic integral and psi(x) is the Chebyshev's psi function.
The present sequence lists the Chebyshev primes that begin a record gap to the next Chebyshev prime.
See A196672 for the length of the gap.

M. Planat and P. Solé, Efficient prime counting and the Chebyshev primes arXiv:1109.6489 [math.NT]

Cf. A002386 (primes beginning a record gap).

Cf. A182876 (Ramanujan primes that begin a record gap to the next Ramanujan prime).

cp's OEIS Frontend

A182873 First differences of the Ramanujan primes, A104272.

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A182877 Record gaps between Ramanujan primes.

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A196673 Chebyshev primes that begin a record gap to the next Chebyshev prime.

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