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.

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A195329 Records of A195325.

Original entry on oeis.org

2, 59, 71, 149, 191, 641, 809, 3371, 5849, 9239, 20507, 20981, 32117, 48779, 176777, 191249, 204509, 211061, 223679, 245129, 358877, 654161, 2342771, 3053291, 4297961, 4755347, 6750221, 8019509, 9750371, 10196759, 11237981, 23367077, 34910219, 93929219, 186635747
Offset: 1

Views

Author

Vladimir Shevelev, Sep 15 2011

Keywords

Comments

The sequence is infinite. Conjecture. For n>=2, all terms are in A001359. This conjecture (weaker than the conjecture in comment to A195325) also implies the twin prime conjecture.

Crossrefs

Cf. A195325, A080192, A195270, A195271, A193507, A194186, A164368, A194598, A194658, A194659, A194674, A164288, A164294.

A195379 3.5-gap primes: Primes prime(k) such that there is no prime between 7*prime(k)/2 and 7*prime(k+1)/2.

Original entry on oeis.org

2, 137, 281, 521, 641, 883, 937, 1087, 1151, 1229, 1277, 1301, 1489, 1567, 1607, 1697, 2027, 2081, 2237, 2381, 2543, 2591, 2657, 2687, 2729, 2801, 2851, 2969, 3119, 3257, 3301, 3359, 3463, 3467, 3529, 3673, 3733, 3793, 3821, 3851, 4073, 4217, 4229, 4241, 4259, 4283, 4337, 4421, 4481
Offset: 1

Views

Author

Vladimir Shevelev, Sep 17 2011

Keywords

Crossrefs

Cf. A080192, A195270, A195271, A195377, A195325, A195329, A193507, A194186, A164368, A194598, A194658, A194659, A194674, A164288, A164294.

Programs

  • Mathematica
    Select[Prime[Range[1000]], PrimePi[7*NextPrime[#]/2] == PrimePi[7*#/2] &] (* T. D. Noe, Sep 20 2011 *)

Extensions

Corrected by R. J. Mathar, Sep 20 2011

A194953 Nonzero values of |A194659(n)-A194186(n+1)|.

Original entry on oeis.org

2, 6, 2, 4, 4, 4, 2, 2, 8, 2, 2, 4, 4, 4, 6, 2, 2, 4, 2, 2, 10, 6, 6, 2, 2, 2, 6, 2, 8, 8, 4, 6, 4, 2, 8, 4, 8, 4, 4, 6, 4, 2, 4, 2, 4, 2, 2, 22, 2, 2, 6, 4, 4, 8, 2, 2, 10, 2, 2, 2, 2, 4, 4, 4, 2, 2, 2, 2, 2, 10, 2, 2, 8, 18, 2, 2, 4, 4, 2, 12, 6, 6, 8, 20
Offset: 1

Views

Author

Vladimir Shevelev, Sep 06 2011

Keywords

Comments

The sequence (together with A194674) characterizes a right-left symmetry in the distribution of primes over intervals (2*p_n, 2*p_(n+1)), n=1,2,..., where p_n is the n-th prime.

Crossrefs

Cf. A104272, A080359, A193507, A194186, A164368, A194598, A194658, A194659, A194674, A164288, A164294.

A182451 Numbers of A166252 which are not in A164554.

Original entry on oeis.org

109, 151, 191, 229, 233, 283, 311, 571, 643, 683, 727, 941, 991, 1033, 1051, 1373, 1493, 1667, 1697, 1741, 1747, 1783, 1787, 1801, 1931
Offset: 1

Views

Author

Vladimir Shevelev, Apr 29 2012

Keywords

Comments

All Ramanujan primes (A104272) are in A164368 and all Labos primes (A080359) are in A194598. Peculiar primes (see comment in A164554)are simultaneously Ramanujan and Labos primes, while central primes (A166252) are in the intersection of A164368 and A194598 for n>=2. Hence, for n>=2, all peculiar primes are central primes, but conversely is not true. The sequence lists non-peculiar central numbers.

Crossrefs

Cf. A164554, A166252, A104272, A080359, A164368, A194598.
Previous Showing 11-14 of 14 results.

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