A390983 The smallest prime whose representation in base n contains the digit 0.

2, 3, 17, 5, 37, 7, 67, 83, 101, 11, 149, 13, 197, 227, 257, 17, 331, 19, 401, 443, 487, 23, 577, 631, 677, 733, 787, 29, 907, 31, 1031, 1091, 1163, 1229, 1297, 37, 1447, 1523, 1601, 41, 1777, 43, 1949, 2027, 2129, 47, 2309, 2411, 2503, 2609, 2707, 53, 2917

Offset

2,1

Comments

If n is prime then a(n) = n, otherwise a(n) > n^2.

Such a prime always exists.

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Mathematica

A390983[n_] := If[PrimeQ[n], n, NestWhile[NextPrime, NextPrime[n^2], FreeQ[IntegerDigits[#, n], 0] &]];
Array[A390983, 60, 2] (* Paolo Xausa, Dec 01 2025 *)

Prog

(PARI) a(n) = my(p=2); while (vecmin(digits(p, n)), p = nextprime(p+1)); p; \\ Michel Marcus, Nov 25 2025

Crossrefs

Sequence in context: A140383 A029913 A073125 * A171240 A078201 A361104

Adjacent sequences: A390980 A390981 A390982 * A390984 A390985 A390986

Keyword

nonn,base

Author

Nicolas Bělohoubek, Nov 25 2025

Status

approved