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

1,1

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000040, A380811, A380883.

Sequence in context: A366358 A245242 A004096 * A156152 A106885 A072439

Adjacent sequences: A380880 A380881 A380883 * A380885 A380886 A380887

Keyword

nonn,base,new

Author

David James Sycamore, Feb 07 2025

Extensions

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

Status

approved