A306155 a(n) > a(n-1) is the smallest number such that a(n)! contains a(n-1)! as a substring, with a(0) = 0.

0, 1, 5, 14, 179472

Offset

0,3

Comments

a(5) = A086654(179472). 179472! has 865005 digits, so this requires finding a substring of that length in a larger factorial. - Ole Egil Skotheim, Mar 16 2026

Links

Table of n, a(n) for n=0..4.

Formula

a(n) = A086654(a(n-1)) for n >= 1, with a(0) = 0. - Ole Egil Skotheim, Mar 16 2026

Example

a(2)=5 and 5! = 120 is a substring of 14! = 8717829(120)0. Therefore, a(3) is 14.

Mathematica

a[0]=0;
a[n_]:=Module[{k=a[n-1]+1}, While[StringPosition[ToString[k!], ToString[a[n-1]!]]=={}, k++]; k];
a/@Range[0, 3]

Crossrefs

Cf. A000142, A086654.

Sequence in context: A156219 A000331 A353610 * A082269 A367030 A107776

Adjacent sequences: A306152 A306153 A306154 * A306156 A306157 A306158

Keyword

nonn,base,more,bref

Author

Ivan N. Ianakiev, Jun 23 2018

Status

approved