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%I #35 Apr 03 2023 10:36:13
%S 2,3,6,10,14,31,38,40,92,94,224,265,305,347,375,442,542,1326,2131,
%T 2749,3837,5461,10194,23128,24414,24960,25536,38828,48819
%N Numbers k such that P = 2^k - 1 - Sum_{primes p<k} 2^(p-1) is prime.
%C These primes P have k binary digits, all equal to 1 except for digits 0 at prime positions (reading from the right, with 2^0 being position 1, 2^1 being position 2, etc.).
%C Sequence A215888 is a variant of the same idea, where positions are counted from 0 on.
%H G. L. Honaker Jr. and Chris Caldwell (Eds.), <a href="https://t5k.org/curios/page.php?short=5461">Prime curio for 5461</a>.
%e a(3) = 6 is in the sequence because 2^6 - 1 - 2^(2 - 1) - 2^(3 - 1) - 2^(5 - 1) = 41 is prime; 41 = 101001_2 has 6 binary digits which are zero in the 2nd, 3rd and 5th position (from the right), and 1's in the other positions.
%t Select[Range[500], PrimeQ[2^# - 1 - Sum[2^(Prime[i] - 1), {i, PrimePi[# - 1]}]] &] (* _Alonso del Arte_, Aug 25 2012 *)
%o (PARI) is_A215891(N)=ispseudoprime(2^N-1-sum(n=1,primepi(N-1),2^(prime(n)-1)))
%K nonn,nice,hard,more
%O 1,1
%A _M. F. Hasler_, Aug 25 2012
%E a(23) from _Jon E. Schoenfield_, Jul 08 2015
%E a(24)-a(27) from _Jon E. Schoenfield_, Feb 15 2021
%E a(28)-a(29) from _Amiram Eldar_, Feb 20 2021
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