A380884 Primes p such that there is an m < 10 for which m*p contains every decimal digit of p.

2, 5, 41, 43, 59, 97, 191, 197, 251, 263, 373, 401, 443, 491, 499, 599, 653, 691, 967, 991, 997, 1481, 1901, 1913, 1997, 2549, 2551, 2591, 3067, 3491, 4001, 4013, 4493, 4793, 4931, 4943, 4967, 4973, 4993, 4999, 5021, 5443, 5647, 6053, 6361, 6521, 6703, 6991, 7489, 7901, 7951, 7993

Offset: 1

Author

David James Sycamore, Feb 07 2025

Keywords

• nonn
• base

Examples

			6*2 = 12 therefore 2 is a term (m = 6 < 10).
499*6 = 2994 therefore 499 is a term (m = 6 < 10).
599*5 = 2995 therefore 599 is a term (m = 5 < 10).
37 is not a term since 10*37 = 370 is the smallest multiple of 37 containing 3 and 7
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000040, A380811, A380883.

Programs

Mathematica

nn = 10000; Reap[Do[p = Prime[n]; d = DigitCount[p]; k = 2; While[! AllTrue[DigitCount[#] - d, # >= 0 &] &[p*k], k++]; If[k < 10, Sow[p]], {n, nn}]][[-1, 1]] (* Michael De Vlieger, Feb 20 2025 *)

PARI

lista(nn) = forprime(p=2, nn, if (A380883(p) != 10*p, print1(p, ", "))); \\ Michel Marcus, Feb 20 2025

Extensions

59, 491, and more terms added by Michel Marcus, Feb 20 2025