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

2,1

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A037153 A323185 A168065 * A163867 A077381 A225636

Adjacent sequences: A077721 A077722 A077723 * A077725 A077726 A077727

Keyword

nonn

Author

Amarnath Murthy, Nov 19 2002

Extensions

More terms from Sascha Kurz, Jan 03 2003

Status

approved