The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A215891 Numbers k such that P = 2^k - 1 - Sum_{primes p
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS G. L. Honaker Jr. and Chris Caldwell (Eds.), Prime curio for 5461. EXAMPLE 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. MATHEMATICA Select[Range[500], PrimeQ[2^# - 1 - Sum[2^(Prime[i] - 1), {i, PrimePi[# - 1]}]] &] (* Alonso del Arte, Aug 25 2012 *) PROG (PARI) is_A215891(N)=ispseudoprime(2^N-1-sum(n=1, primepi(N-1), 2^(prime(n)-1))) CROSSREFS Sequence in context: A337611 A325724 A111467 * A254033 A102366 A152452 Adjacent sequences:  A215888 A215889 A215890 * A215892 A215893 A215894 KEYWORD nonn,nice,hard,more AUTHOR M. F. Hasler, Aug 25 2012 EXTENSIONS 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 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 1 22:23 EDT 2022. Contains 354984 sequences. (Running on oeis4.)