A179481 -id:A179481 - cp's OEIS frontend

A179687 a(n) = 2*q(n)-1 where q(n) is the sequence of records positions of A179686.

3, 5, 7, 19, 27, 37, 47, 53, 67, 95, 101, 103, 107, 131, 149, 173, 181, 191, 227, 239, 263, 293, 311, 317, 349, 359, 367, 373, 383, 419, 461, 463, 479, 509, 547, 557, 587, 613, 619, 647, 653, 677, 701, 743, 751, 773, 787, 821, 841, 863, 887, 947

Offset: 1

Vladimir Shevelev, Jul 24 2010

nonn

The record positions are q(n) = 2, 3, 4, 10, 14, 19, 24, 27, 34,...

Sequences A179382, A179383, A179480, A179481, A179686 and this sequence show that their terms depend on prime power factorization of 2*n-1. Nevertheless, this question yet is waiting its research. Most likely that almost all terms of this sequence are primes (27, 95, 841,... are not).

Cf. A179382, A179383, A179480, A179481, A179686

Extended beyond a(7) by R. J. Mathar, Dec 04 2011

A179538 Numbers 2n+1 for which A003558(n), n>=1, are record values of A003558.

Original entry on oeis.org

3, 5, 7, 11, 13, 19, 23, 29, 37, 47, 53, 59, 61, 67, 71, 79, 83, 101, 103, 107, 121, 131, 139, 149, 163, 167, 173, 179, 181, 191, 197, 199, 211, 227, 239, 263, 269, 271, 293, 311, 317, 347, 349, 359, 367, 373, 379, 383, 389, 419, 421, 443, 461, 463, 467, 479

Offset: 1

Vladimir Shevelev, Jul 18 2010

nonn

Conjecture. All terms are primes except for a finite set of squares of primes.

All terms from a(1) to a(5000) are primes except for a(21) = 121 = 11^2, supporting V. Shevelev's conjecture. [John W. Layman, Jul 22 2010]

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A003558, A139099, A179383, A179481.

s = {}; am = 0; Do[a = Min[MultiplicativeOrder[2, n, {-1, 1}]]; If[a > am, am = a; AppendTo[s, n]], {n, 3, 480, 2}]; s (* Amiram Eldar, Sep 13 2019 *)

a(31)-a(56) from John W. Layman, Jul 22 2010

A179739 a(n) = 2*h(n)-1 where h(n) is the sequence of records positions of A179738.

Original entry on oeis.org

3, 5, 7, 11, 13, 31, 37

Offset: 2

Vladimir Shevelev, Jul 25 2010

nonn

Cf. A179738 A179382, A179383, A179480, A179481, A179686 A179687

A179788 2*r(n)-1 where r(n) is the sequence of records positions of A179787.

Original entry on oeis.org

1, 7, 9, 23, 25, 33, 39, 41, 57, 71, 105, 119, 135, 151, 169, 183, 185, 199, 217, 231, 263, 265, 281, 297, 311, 343, 359, 375, 377, 391, 423, 441, 471, 505, 519, 535

Offset: 1

Vladimir Shevelev, Jul 27 2010

nonn

r(n) = 1, 4, 5, 12, 13, 17, 20, 21, 29, 36, 53, 60, 68, 76, 85, 92, 93,...

Cf. A179787, A179383, A179480, A179481, A179686, A179687 A179738, A179739

Values a(2)-a(9) corrected, a(10) etc added by R. J. Mathar, Nov 04 2010

cp's OEIS Frontend

A179687 a(n) = 2*q(n)-1 where q(n) is the sequence of records positions of A179686.

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A179538 Numbers 2n+1 for which A003558(n), n>=1, are record values of A003558.

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A179739 a(n) = 2*h(n)-1 where h(n) is the sequence of records positions of A179738.

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A179788 2*r(n)-1 where r(n) is the sequence of records positions of A179787.

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