%I #13 Mar 14 2023 03:39:41
%S 6,10,22,30,34,58,66,118,618,730,874,1353,2554,2937,7874,7954,8842,
%T 11922,12430,15442,17186,26034,115690,166774,170134,221002,264094,
%U 368599,1419045,1443118,1582026,1583759,1587721,1829929,1934249,2053321,2160359,2207345
%N Numbers n such that 2^n'-1 is prime, where n' is the arithmetic derivative of n.
%C These numbers are the anti-derivatives of the Mersenne primes A000043. The prime 86243 has 11 anti-derivatives! - _T. D. Noe_, May 04 2011
%e 6'=5, 2^5-1=31 = prime -> a(1) = 6
%p 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);
%Y Cf. A000043, A001348, A003415.
%K nonn
%O 1,1
%A _Giorgio Balzarotti_, May 03 2011
%E Extended by _T. D. Noe_, May 04 2011