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A243442 Primes p such that, in base 2, p - digitsum(p) is also a prime. 1
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.

PROG

(PARI) isok(n) = isprime(n) && isprime(n - hammingweight(n)); \\ Michel Marcus, Jun 05 2014

CROSSREFS

Cf. A243441.

Sequence in context: A106956 A084671 A284648 * 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 February 21 12:10 EST 2018. Contains 299411 sequences. (Running on oeis4.)