A240695 a(n) is the smallest k such that a unique product of distinct terms of A050376 which is equal to k! contains at least the first n terms of A050376.

2, 3, 4, 5, 125, 125, 138, 220, 220, 1766, 5526, 10351, 12365, 65653, 65653, 202738, 490333, 808762, 1478432, 1971352, 1971352, 1971352, 14798206, 14798206, 14798206, 14798206, 161974053, 547880880, 1619543840, 1619543840, 1619543840, 2103844465, 6435961044

Offset

1,1

Comments

By the definition, the representation of a(n)! as a product of distinct terms of A050376 should contain the first n terms of A050376 and there is no restriction on the distribution of other factors of this product.

a(38) > 2 * 10^11. - Hiroaki Yamanouchi, Oct 01 2014

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..37

Example

5! = 2*3*4*5. We have the first 4 terms of A050376, so a(4) = 5.

Mathematica

bad[n_, pp_, mo_] := Catch[Do[If[ Mod[(n - Total@ IntegerDigits[n, pp[[i]]]) /(pp[[i]] - 1), mo[[i]] + 1] != mo[[i]], Throw@ True], {i, Length@ pp}]; False]; a[n_]:= Block[{fa, mo, pp, k}, fa = FactorInteger[ Times @@ Select[Range[2, Prime[n]], (f = FactorInteger@# ; Length[f] == 1 && IntegerQ[Log[2, f[[1, 2]]]]) &, n]]; pp = First /@ fa; mo = Last /@ fa; k = fa[[-1, 1]]; While[ bad[k, pp, mo], k++]; k]; Array[a, 15] (* Giovanni Resta, Apr 11 2014 *)

Crossrefs

Cf. A240537, A240606, A240619, A240620, A240668, A240669, A240670, A240672.

Sequence in context: A010348 A171591 A140432 * A004867 A318842 A298671

Adjacent sequences: A240692 A240693 A240694 * A240696 A240697 A240698

Keyword

nonn

Author

Vladimir Shevelev, Apr 10 2014

Extensions

a(5)-a(23) from Giovanni Resta, Apr 11 2014

a(24)-a(33) from Hiroaki Yamanouchi, Oct 01 2014

Status

approved