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

%I A380884 #13 Feb 23 2025 11:18:23
%S A380884 2,5,41,43,59,97,191,197,251,263,373,401,443,491,499,599,653,691,967,
%T A380884 991,997,1481,1901,1913,1997,2549,2551,2591,3067,3491,4001,4013,4493,
%U A380884 4793,4931,4943,4967,4973,4993,4999,5021,5443,5647,6053,6361,6521,6703,6991,7489,7901,7951,7993
%N A380884 Primes p such that there is an m < 10 for which m*p contains every decimal digit of p.
%H A380884 Michael De Vlieger, <a href="/A380884/b380884.txt">Table of n, a(n) for n = 1..5000</a>
%e A380884 6*2 = 12 therefore 2 is a term (m = 6 < 10).
%e A380884 499*6 = 2994 therefore 499 is a term (m = 6 < 10).
%e A380884 599*5 = 2995 therefore 599 is a term (m = 5 < 10).
%e A380884 37 is not a term since 10*37 = 370 is the smallest multiple of 37 containing 3 and 7
%t A380884 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 *)
%o A380884 (PARI) lista(nn) = forprime(p=2, nn, if (A380883(p) != 10*p, print1(p, ", "))); \\ _Michel Marcus_, Feb 20 2025
%Y A380884 Cf. A000040, A380811, A380883.
%K A380884 nonn,base
%O A380884 1,1
%A A380884 _David James Sycamore_, Feb 07 2025
%E A380884 59, 491, and more terms added by _Michel Marcus_, Feb 20 2025