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A337497 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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

LINKS

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.

EXAMPLE

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.

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A337496, A337536.

Sequence in context: A038884 A338345 A252282 * A040122 A318207 A038955

Adjacent sequences:  A337494 A337495 A337496 * A337498 A337499 A337500

KEYWORD

nonn,base,hard

AUTHOR

François Marques, Aug 29 2020

STATUS

approved

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Last modified February 27 05:37 EST 2021. Contains 341649 sequences. (Running on oeis4.)