A337770 - OEIS

%I #18 Jun 04 2022 21:18:37

%S 1,1,2,6,24,104,604,4204,32204,272204,2072204,22072204,242072204,

%T 2642072204,28642072204,308642072204,4808642072204,68808642072204,

%U 1088808642072204,19088808642072204,209088808642072204,4209088808642072204,88209088808642072204

%N 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).

%C 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.

%C 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.

%H Harvey P. Dale, <a href="/A337770/b337770.txt">Table of n, a(n) for n = 0..468</a>

%e As a(4) is 24, a(5) is {2*5, 4} which is 104, where {x, y} is the concatenation of x and y.

%e a(7) is 4204, a(8) is {4*8, 204} which is 32204.

%t 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 *)

%o (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

%Y Cf. A000142, A089718.

%K nonn,base,easy

%O 0,3

%A _Jamie Robert Creasey_, Sep 19 2020