A321392 a(n) is the number of bases b > 1 such that prime(n) + digitsum(prime(n), base b) is prime (where prime(n) denotes the n-th prime number).

1, 1, 2, 1, 2, 3, 4, 4, 3, 5, 6, 7, 7, 7, 7, 10, 11, 10, 12, 11, 11, 12, 11, 13, 16, 14, 13, 10, 14, 13, 21, 19, 19, 17, 20, 21, 24, 26, 25, 25, 25, 23, 26, 26, 24, 26, 29, 33, 27, 30, 31, 28, 32, 33, 32, 34, 34, 34, 32, 31, 34, 37, 37, 41, 36, 38, 41, 44, 45

Offset

1,3

Comments

For any prime number p and base b > p, p + digitsum(p, base b) equals twice p and is not prime, hence the sequence is well defined.

For prime(n) + digitsum(prime(n), base b) to be prime, b must be even (see A320866).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored scatterplot of (n, b) such that prime(n) + sumdigits(prime(n), base 2*b) is prime and 1 <= n <= 2000 and 1 <= b <= 1000 (where the color is function of floor(prime(n) / (2*b)))

Formula

a(n) = A321393(A000040(n)).

Example

For n = 6, we have prime(6) = 13 and:
  b     13 + sumdigits(13, base b)
  ----  --------------------------
     2  16
     4  17 (prime)
     6  16
     8  19 (prime)
    10  17 (prime)
    12  15
  >=14  26
Hence, a(6) = 3.

Prog

(PARI) a(n) = my (p=prime(n)); sum(b=1, p\2, isprime(p+sumdigits(p, 2*b)))

Crossrefs

Cf. A000040, A243441, A320866, A321393.

Sequence in context: A241419 A203108 A230989 * A030339 A030383 A031231

Adjacent sequences: A321389 A321390 A321391 * A321393 A321394 A321395

Keyword

nonn,base

Author

Rémy Sigrist, Nov 08 2018

Status

approved