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A380884
Primes p such that there is an m < 10 for which m*p contains every decimal digit of p.
1
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
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
KEYWORD
nonn,base,new
AUTHOR
EXTENSIONS
59, 491, and more terms added by Michel Marcus, Feb 20 2025
STATUS
approved