

A337770


a(0)=1; a(n) is the leading digit of a(n1) multiplied by n concatenated with the remaining digits of a(n1).


2



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

0,3


COMMENTS

This sequence bears similarities to the digit factorials, see A089718. However, unlike the digit factorials, we only multiply the leading digit of a(n1) by n, instead of all digits present. As such, for indices greater than 4, a(n) includes all the digits from a(n1), except those resulting from the lead digit of a(n1) being multiplied by n.
If one attempts this with the last digit of a(n1) 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.


LINKS



EXAMPLE

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.


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 *)


PROG

(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 + (th)); v} \\ Andrew Howroyd, Sep 19 2020


CROSSREFS



KEYWORD

nonn,base,easy


AUTHOR



STATUS

approved



