A308439 a(n) is the smallest prime factor of 1 + the product of primes indexed by the binary digits of n.

3, 2, 7, 2, 11, 2, 31, 2, 3, 2, 43, 2, 71, 2, 211, 2, 23, 2, 67, 2, 3, 2, 331, 2, 5, 2, 463, 2, 3, 2, 2311, 2, 3, 2, 79, 2, 131, 2, 17, 2, 3, 2, 547, 2, 911, 2, 2731, 2, 7, 2, 859, 2, 3, 2, 7, 2, 2003, 2, 6007, 2, 3, 2, 59, 2, 5, 2, 103, 2, 3, 2, 7, 2, 239

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

a(n) = A020639(A019565(n) + 1). - Michel Marcus, Jun 02 2019

Example

a(1) = a(01_2) = 2^1 * 3^0 + 1 = 3;
a(2) = a(10_2) = 2^0 * 3^1 + 1 = 2^2 = 2;
a(3) = a(11_2) = 2^1 * 3^1 + 1 = 7.

Prog

(PARI) a(n) = {my(b = binary(n), x = 1 + prod(k=1, #b, prime(#b-k+1)^b[k])); factor(x)[1, 1]; } \\ Michel Marcus, Jun 02 2019
(Python)
from functools import reduce
from operator import mul
from sympy import prime, primefactors
def A308439(n):
    return min(primefactors(1 + reduce(mul, (prime(i+1) for i, j in enumerate(bin(n)[:1:-1]) if j == '1')))) # Chai Wah Wu, Jun 03 2019

Crossrefs

Cf. A000945, A019565, A020639.

Sequence in context: A265219 A349211 A266664 * A245601 A355934 A296513

Adjacent sequences: A308436 A308437 A308438 * A308440 A308441 A308442

Keyword

nonn,base

Author

Brendan Hickey, May 27 2019

Status

approved