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A337497
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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.
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1
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0, 1, 2, 5, 7, 11, 19, 39, 23, 69, 103, 47, 59, 125, 95, 143, 119, 179, 299, 251, 335, 527, 239, 419, 599, 359, 479, 1019, 671, 1619, 1727, 959, 719, 1319, 839, 2039, 1259, 2771, 2339, 2099, 1439, 5471, 1679, 2159, 3695, 3599, 2879, 5939, 3779, 2519, 4619, 3359, 4319
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OFFSET
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0,3
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COMMENTS
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a(n) = Min_({k | A337496(k)=n}) if the set is not empty, else -1.
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.
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LINKS
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François Marques, Table of n, a(n) for n = 0..3443
François Marques, Table of known a(n) values, for n = 0..10000. Unknown values are replaced by a question mark.
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A337496, A337536.
Sequence in context: A038884 A338345 A252282 * A040122 A318207 A038955
Adjacent sequences: A337494 A337495 A337496 * A337498 A337499 A337500
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KEYWORD
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nonn,base,hard
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AUTHOR
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François Marques, Aug 29 2020
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STATUS
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approved
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