A189992 Numbers n such that 2^n'-1 is prime, where n' is the arithmetic derivative of n.

6, 10, 22, 30, 34, 58, 66, 118, 618, 730, 874, 1353, 2554, 2937, 7874, 7954, 8842, 11922, 12430, 15442, 17186, 26034, 115690, 166774, 170134, 221002, 264094, 368599, 1419045, 1443118, 1582026, 1583759, 1587721, 1829929, 1934249, 2053321, 2160359, 2207345

Offset

1,1

Comments

These numbers are the anti-derivatives of the Mersenne primes A000043. The prime 86243 has 11 anti-derivatives! - T. D. Noe, May 04 2011

Links

Table of n, a(n) for n=1..38.

Example

6'=5, 2^5-1=31 = prime -> a(1) = 6

Maple

last:=120: der:=n->n*add(op(2, p)/op(1, p), p=ifactors(n)[2]): seq(`if`(isprime(2^(der(i))- 1)=true, i, NULL), i=2..last);

Crossrefs

Cf. A000043, A001348, A003415.

Sequence in context: A369656 A365064 A157037 * A255746 A082917 A001172

Adjacent sequences: A189989 A189990 A189991 * A189993 A189994 A189995

Keyword

nonn

Author

Giorgio Balzarotti, May 03 2011

Extensions

Extended by T. D. Noe, May 04 2011

Status

approved