A287945 a(n) = largest prime q such that q | 2^p - 2 and p - 1 | q - 1, where p = prime(n).

2, 3, 5, 7, 31, 13, 257, 73, 683, 113, 331, 109, 61681, 5419, 2796203, 1613, 3033169, 1321, 599479, 122921, 38737, 22366891, 8831418697, 2931542417, 22253377, 268501, 131071, 28059810762433, 279073, 54410972897, 77158673929, 145295143558111, 2879347902817, 10052678938039, 616318177, 1133836730401, 121369

Offset

1,1

Comments

First conjecture: a(n) > prime(n) for all n > 6. Robert Israel tested the author's conjecture up to prime(95) = 499. The prime factorizations of the numbers 2^(p-1)-1 for larger p can be checked in available tables, see A005420.

Second conjecture: a(n) = gpf(2^prime(n) - 2) for almost all n, in the sense that the set of exceptions {10, 16, 37, 40, ...} has zero natural density.

Primes p for which p - 1 does not divide gpf(2^p - 2) - 1 are 29, 53, 157, 173, ...

Links

Table of n, a(n) for n=1..37.

Example

For prime(5) = 11, 2^11-2 = 2*3*11*31 and 11-1 | 31-1, so a(5) = 31.

Crossrefs

Cf. A000040, A005420.

Sequence in context: A174536 A054797 A297710 * A238850 A245064 A052014

Adjacent sequences: A287942 A287943 A287944 * A287946 A287947 A287948

Keyword

nonn

Author

Thomas Ordowski, Sep 01 2017

Status

approved