A103782 a(n) = minimal m >= 0 that makes primorial P(n)*2^m-1 prime.

0, 0, 1, 0, 0, 1, 1, 2, 3, 12, 1, 0, 22, 2, 4, 13, 12, 6, 1, 4, 1, 4, 0, 2, 9, 5, 6, 2, 1, 9, 17, 22, 7, 19, 73, 23, 12, 5, 27, 33, 64, 33, 5, 7, 41, 44, 35, 29, 3, 19, 6, 26, 5, 11, 9, 33, 34, 16, 63, 46, 8, 4, 24, 48, 0, 11, 0, 26, 6, 25, 17, 31, 6, 46, 33, 46, 17, 8, 61, 12, 23, 76, 20, 17

Offset

2,8

Comments

The values of n in A103515

Links

Table of n, a(n) for n=2..85.

Example

P(2)*2^0-1=5 is prime, so a(2)=0; P(9)*2^2-1=892371479 is prime, so a(9)=2;

Mathematica

nmax = 2^2048; npd = 2; n = 2; npd = npd*Prime[n]; While[npd < nmax, tn = 0; tt = 1; cp = npd*tt - 1; While[(cp > 1) && (! (PrimeQ[cp])), tn = tn + 1; tt = tt*2; cp = npd*tt - 1]; Print[tn]; n = n + 1; npd = npd*Prime[n]]

Crossrefs

Cf. A002110, A005234, A014545, A018239, A006794, A057704, A057705, A103513, A103515.

Sequence in context: A072928 A140970 A058523 * A128438 A286202 A286413

Adjacent sequences: A103779 A103780 A103781 * A103783 A103784 A103785

Keyword

nonn

Author

Lei Zhou, Feb 15 2005

Status

approved