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

Author

Rémy Sigrist, Nov 08 2018

Keywords

• nonn
• base

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).

Examples

			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.
		

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)))

Crossrefs

Cf. A000040, A243441, A320866, A321393.

Programs

PARI

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

Formula

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