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A215891
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Numbers k such that P = 2^k - 1 - Sum_{primes p<k} 2^(p-1) is prime.
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1
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2, 3, 6, 10, 14, 31, 38, 40, 92, 94, 224, 265, 305, 347, 375, 442, 542, 1326, 2131, 2749, 3837, 5461, 10194, 23128, 24414, 24960, 25536, 38828, 48819
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OFFSET
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1,1
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COMMENTS
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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.).
Sequence A215888 is a variant of the same idea, where positions are counted from 0 on.
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LINKS
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Table of n, a(n) for n=1..29.
G. L. Honaker Jr. and Chris Caldwell (Eds.), Prime curio for 5461.
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range[500], PrimeQ[2^# - 1 - Sum[2^(Prime[i] - 1), {i, PrimePi[# - 1]}]] &] (* Alonso del Arte, Aug 25 2012 *)
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PROG
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(PARI) is_A215891(N)=ispseudoprime(2^N-1-sum(n=1, primepi(N-1), 2^(prime(n)-1)))
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CROSSREFS
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Sequence in context: A337611 A325724 A111467 * A254033 A102366 A152452
Adjacent sequences: A215888 A215889 A215890 * A215892 A215893 A215894
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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M. F. Hasler, Aug 25 2012
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EXTENSIONS
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a(23) from Jon E. Schoenfield, Jul 08 2015
a(24)-a(27) from Jon E. Schoenfield, Feb 15 2021
a(28)-a(29) from Amiram Eldar, Feb 20 2021
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STATUS
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approved
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