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 A243442 Primes p such that, in base 2, p - digitsum(p) is also a prime. 8
 5, 23, 71, 83, 101, 113, 197, 281, 317, 353, 359, 373, 401, 467, 599, 619, 683, 739, 751, 773, 977, 1091, 1097, 1103, 1217, 1223, 1229, 1237, 1283, 1303, 1307, 1429, 1433, 1489, 1553, 1559, 1601, 1607, 1613, 1619, 1699, 1873, 1879, 2039, 2347, 2357, 2389 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS In all bases b, x = n - digitsum(n) is always divisible by b-1, therefore x can be prime only in base 2 and bases b for which b-1 is prime. For example, in base 10, n - digitsum(n) is always divisible by 10 - 1 = 9 -- see A066568 and A068395. In base 8, 9 = 11, therefore 11 - digitsum(11) = 9 - 2 = 7 is divisible by 7. LINKS Anthony Sand, Table of n, a(n) for n = 1..1000 EXAMPLE 5 - digitsum(5,base=2) = 5 - digitsum(101) = 5 - 2 = 3. 23 - digitsum(10111) = 23 - 4 = 19. 71 - digitsum(1000111) = 71 - 4 = 67. 83 - digitsum(1010011) = 83 - 4 = 79. 101 - digitsum(1100101) = 101 - 4 = 97. MATHEMATICA Select[Prime[Range[400]], PrimeQ[#-Total[IntegerDigits[#, 2]]]&] (* Harvey P. Dale, May 15 2019 *) PROG (PARI) isok(n) = isprime(n) && isprime(n - hammingweight(n)); \\ Michel Marcus, Jun 05 2014 CROSSREFS Cf. A243441. Sequence in context: A084671 A284648 A290187 * A064395 A230497 A138905 Adjacent sequences:  A243439 A243440 A243441 * A243443 A243444 A243445 KEYWORD nonn,base AUTHOR Anthony Sand, Jun 05 2014 STATUS approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)