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%I #49 Nov 27 2020 11:24:49
%S 0,1,2,5,7,11,19,39,23,69,103,47,59,125,95,143,119,179,299,251,335,
%T 527,239,419,599,359,479,1019,671,1619,1727,959,719,1319,839,2039,
%U 1259,2771,2339,2099,1439,5471,1679,2159,3695,3599,2879,5939,3779,2519,4619,3359,4319
%N a(n) is the smallest integer k with exactly n bases b such that k in base b contains the digit b-1; or -1 if there is no such integer.
%C a(n) = Min_({k | A337496(k)=n}) if the set is not empty, else -1.
%C Conjecture: a(n) > log(n)^(sqrt(2)*log(n)) for n>1. This have been checked for n<3444, and for n<10275 unless if a(n)=-1.
%H François Marques, <a href="/A337497/b337497.txt">Table of n, a(n) for n = 0..3443</a>
%H François Marques, <a href="/A337497/a337497_2.txt">Table of known a(n) values, for n = 0..10000</a>. Unknown values are replaced by a question mark.
%e a(7) is 39 because 39 has 7 bases b (which are 2,4,5,8,10,20 and 40) where the digits of n contain the digit b-1 and this does not happen for a smaller integer.
%t mainBaseQ[n_, b_] := MemberQ[IntegerDigits[n, b], b - 1]; basesCount[n_] := Count[Range[2, n + 1], _?(mainBaseQ[n, #] &)]; m = 50; seq = Table[-1, {m}]; c = 0; n = 0; While[c < m, i = basesCount[n]; If[i <= m - 1 && seq[[i + 1]] < 0, c++; seq[[i + 1]] = n]; n++]; seq (* _Amiram Eldar_, Sep 01 2020 *)
%o (PARI) a(n) = for(k=0,+oo, if(sum(b=2, k+1, vecmax(digits(k, b)) == b-1)==n, return(k)) ); \\ _François Marques_, Nov 19 2020
%Y Cf. A337496, A337536.
%K nonn,base,hard
%O 0,3
%A _François Marques_, Aug 29 2020
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