A337770 a(0)=1; a(n) is the leading digit of a(n-1) multiplied by n concatenated with the remaining digits of a(n-1).

1, 1, 2, 6, 24, 104, 604, 4204, 32204, 272204, 2072204, 22072204, 242072204, 2642072204, 28642072204, 308642072204, 4808642072204, 68808642072204, 1088808642072204, 19088808642072204, 209088808642072204, 4209088808642072204, 88209088808642072204

Offset: 0

Author

Jamie Robert Creasey, Sep 19 2020

Keywords

• nonn
• base
• easy

Comments

This sequence bears similarities to the digit factorials, see A089718. However, unlike the digit factorials, we only multiply the leading digit of a(n-1) by n, instead of all digits present. As such, for indices greater than 4, a(n) includes all the digits from a(n-1), except those resulting from the lead digit of a(n-1) being multiplied by n.

If one attempts this with the last digit of a(n-1) instead, 220 is the largest integer reached by the process. All indices greater than 4 yield the same number, as the last digit of 220 is 0 which, if multiplied by 5, results in itself and, if other digits remain consistent, causes 220 to repeat infinitely.

Examples

			As a(4) is 24, a(5) is {2*5, 4} which is 104, where {x, y} is the concatenation of x and y.
a(7) is 4204, a(8) is {4*8, 204} which is 32204.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..468

Crossrefs

Cf. A000142, A089718.

Programs

Mathematica

nxt[{n_,a_}]:=Module[{ida=IntegerDigits[a]},{n+1,ida[[1]](n+1)10^(Length[ ida]-1)+FromDigits[Rest[ida]]}]; NestList[nxt,{0,1},25][[All,2]] (* Harvey P. Dale, Nov 13 2021 *)

PARI

seq(n)={my(v=vector(n+1)); v[1]=1; for(n=1, n, my(t=v[n], b=10^logint(t,10), h=t\b*b); v[n+1] = h*n + (t-h)); v} \\ Andrew Howroyd, Sep 19 2020