A077724 a(n) = smallest prime which can be expressed as a sum of distinct powers of n.

2, 3, 5, 5, 7, 7, 73, 739, 11, 11, 13, 13, 197, 241, 17, 17, 19, 19, 401, 463, 23, 23, 577, 10171901, 677, 757, 29, 29, 31, 31, 32801, 1123, 1336337, 44101, 37, 37, 1483, 59359, 41, 41, 43, 43, 85229, 93151, 47, 47, 110641, 13847169701, 2551, 345157903, 53, 53

Offset: 2

Author

Amarnath Murthy, Nov 19 2002

Keywords

• nonn

Comments

a(n) = smallest prime whose base n representation contains only zeros and 1's.

Values of n at which a(n) reach record values are: 2, 3, 4, 6, 8, 9, 25, 49, 91, 121, 187, 201, 301, 721, 799, 841... Notably, many of them are squares of primes. - Ivan Neretin, Sep 20 2017

Links

• Ivan Neretin, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A020449, A000695, A033046, A077717, A077718, A077719, A077720, A077721, A077722, A077723.

Programs

Mathematica

Table[i = p = 1; While[! PrimeQ[p], p = FromDigits[IntegerDigits[i++, 2], n]]; p, {n, 2, 53}] (* Ivan Neretin, Sep 20 2017 *)

Python

from itertools import count
from sympy import isprime
def A077724(n): return next(filter(isprime,(sum(n**i for i, j in enumerate(bin(m)[-1:1:-1]) if j=='1') for m in count(1)))) # Chai Wah Wu, Apr 04 2025

Extensions

More terms from Sascha Kurz, Jan 03 2003