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

Author

Vladimir Shevelev, Apr 10 2014

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

Extensions

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

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