

A189992


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


0



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
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OFFSET

1,1


COMMENTS

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


LINKS

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


EXAMPLE

6'=5, 2^51=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: A082419 A102783 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



