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%I #26 Feb 21 2021 20:56:10
%S 101,11,2,3,41,5,23,7,181,19,251,43,127,53,281,29,541,37,83,11551,139,
%T 47,523,1481,157,149,12451,67,59,283,11177,2551,239,1187,1453,79,881,
%U 257,89,1553,2851,199,347,563,1483,277,14551,1753,269,827,853,15551,367
%N Smallest prime whose product of digits (A007954) is the n-th 7-smooth number = A002473(n), with a(0) = 101.
%C For n>=1, equals A107698 without the zeros.
%C 101 is the smallest prime with the digit 0, so A007954(101) = 0 but as 0 is not a 7-smooth number, it is chosen a(0) = 101.
%H Robert Israel, <a href="/A341634/b341634.txt">Table of n, a(n) for n = 0..645</a>
%F a(n) = A107698(A002473(n)) for n>=1. - _Amiram Eldar_, Feb 17 2021
%e 83 is prime, A007954(83) = 8*3 = 24 that is the 18th 7-smooth number, and as no prime < 83 has a product of digits = 24, a(18) = 83.
%t pod[n_] := Times @@ IntegerDigits[n]; seq[max_] := Module[{sm7 = Join[{0}, Select[Range[max], Max[FactorInteger[#][[;; , 1]]] <= 7 &]], m, s, n, c, i, ind}, m = Length[sm7]; s = Table[0, {m}]; n = 1; c = 0; While[c < m, n = NextPrime[n]; i = pod[n]; If[MemberQ[sm7, i], ind = Position[sm7, i][[1, 1]]]; If[s[[ind]] == 0, c++; s[[ind]] = n]]; s]; seq[150] (* _Amiram Eldar_, Feb 16 2021 *)
%Y Cf. A002473, A004954, A007954, A053666, A107698, A335331.
%K nonn,base
%O 0,1
%A _Bernard Schott_, Feb 16 2021
%E More terms from _Amiram Eldar_, Feb 16 2021
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