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
Examples
For n = 6, we have prime(6) = 13 and:
b 13 + sumdigits(13, base b)
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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)))
Programs
-
PARI
a(n) = my (p=prime(n)); sum(b=1, p\2, isprime(p+sumdigits(p, 2*b)))
Comments