A089718 -id:A089718 - cp's OEIS frontend

A110728 Digital factorial: a(0) = 1, a(n) = n * (the sum of the digits of a(n-1)).

1, 1, 2, 6, 24, 30, 18, 63, 72, 81, 90, 99, 216, 117, 126, 135, 144, 153, 162, 171, 180, 189, 396, 414, 216, 225, 234, 243, 252, 261, 270, 279, 576, 594, 612, 315, 324, 333, 342, 351, 360, 369, 756, 774, 792, 810, 414, 423, 432, 441, 450, 459, 936, 954, 972

Offset: 0

Amarnath Murthy, Aug 09 2005

			a(4) = 24, a(5) = 5*(2+4) = 30, a(6) = 6*3 = 18.

Colin Barker, Table of n, a(n) for n = 0..1000

Cf. A000142, A007953, A089718, A110729.

a:= proc(n) option remember; `if`(n=0, 1,
      n*add(i, i=convert(a(n-1), base, 10)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 12 2020

DigitSum[n_, 10] := Total[IntegerDigits[n, 10]]; A110728[0] := 1; A110728[n_] := A110728[n] = n*DigitSum[A110728[n - 1], 10]; Table[A110728[n], {n, 0, 50}] (* G. C. Greubel, Sep 06 2017 *)

s=vector(1001, n, 1); for(n=2, #s, s[n]=(n-1)*sumdigits(s[n-1])); s \\ Colin Barker, Nov 20 2014

a(22) and a(32) corrected, name clarified, and more terms added by Colin Barker, Nov 20 2014

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).

Original entry on oeis.org

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

Jamie Robert Creasey, Sep 19 2020

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.

			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.

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

Cf. A000142, A089718.

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 *)

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

A337016 a(0) = 0. Successive terms are double the previous, then with their digits incremented by 1.

Original entry on oeis.org

0, 1, 3, 7, 25, 61, 233, 577, 2265, 5641, 22393, 55897, 2228105, 5567321, 22245753, 555102617, 2221316345, 55537437101, 222185985313, 5554821081737, 222110753274585, 5553326176510281, 22217763464131673, 555466371039374457, 222110438531898591025

Offset: 0

Jamie Robert Creasey, Nov 21 2020

If 9 appears anywhere in the decimal expansion of 2*a(n-1), we replace that digit with 10 upon incrementing by 1. See a(12) of the Examples section and A216556 for more information.

			To calculate a(12), double 55897 to get 111794, then increment the digits by 1 to get 2228105.
To calculate a(13), double 2228105 to get 4456210, then increment the digits by 1 to get 5567321.

Cf. A000079, A061511, A089718.

a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(seq(
      l[-i]+1, i=1..nops(l)))))(convert(2*a(n-1), base, 10)))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Dec 12 2020

NestList[FromDigits[Flatten@ Map[IntegerDigits, IntegerDigits[2 #] + 1]] &, 0, 24] (* Michael De Vlieger, Dec 11 2020 *)

digs(n) = if (n==0, [0], digits(n));
lista(nn) = {a = 0; print1(a, ", "); for (n=1, nn, a = eval(concat(apply(t->Str(t+1), digs(2*a)))); print1(a, ", "););} \\ Michel Marcus, Nov 28 2020

a(n) = A216556(2*a(n-1)), a(0) = 0.

A338767 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by n.

Original entry on oeis.org

0, 1, 3, 6, 10, 65, 1211, 8988, 16171616, 1015101610151015, 11101115111011161110111511101115, 1212121112121216121212111212121712121211121212161212121112121216

Offset: 0

Jamie Robert Creasey, Nov 07 2020

This sequence is the additive counterpart of the digit factorials which, unlike the digit factorials, increases at a faster pace. A061511 and its relatives bear similarities to this sequence, but each of these increase at varying rates depending on the chosen constant. However, unlike these sequences, the constant increases by 1 each time. If digits within a(n-1) exceed 9 when one adds a constant, we ignore carrying and replace the digit with its correct value, thus 9+1 = 10. a(15) has 1024 digits.

			a(5) = {1+5, 0+5} = 65, where {x, y} is the concatenation of x and y.
a(6) = {6+6, 5+6} = 1211.

Cf. A061511-A061750, A061581-A061587, A089718, A337770.

a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(
      seq(n+l[-i], i=1..nops(l)))))(convert(a(n-1), base, 10)))
    end:
seq(a(n), n=0..12);  # Alois P. Heinz, Nov 15 2020

Nest[Append[#1, FromDigits@ Apply[Join, Map[IntegerDigits, IntegerDigits[#1[[-1]] ] + #2]]] & @@ {#, Length@ #} &, {0}, 11] (* Michael De Vlieger, Nov 13 2020 *)

cp's OEIS Frontend

A110728 Digital factorial: a(0) = 1, a(n) = n * (the sum of the digits of a(n-1)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions

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).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A337016 a(0) = 0. Successive terms are double the previous, then with their digits incremented by 1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A338767 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Mathematica