A063018 -id:A063018 - cp's OEIS frontend

A232486 a(1) = 3; thereafter a(n+1) = a(n) + product of nonzero digits of a(n).

3, 6, 12, 14, 18, 26, 38, 62, 74, 102, 104, 108, 116, 122, 126, 138, 162, 174, 202, 206, 218, 234, 258, 338, 410, 414, 430, 442, 474, 586, 826, 922, 958, 1318, 1342, 1366, 1474, 1586, 1826, 1922, 1958, 2318, 2366, 2582, 2742, 2854, 3174, 3258, 3498, 4362, 4506

Offset: 1

N. J. A. Sloane, Nov 29 2013

P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151.
P. A. Loomis, An Introduction to Digit Product Sequences, J. Rec. Math., 32 (2003-2004), 147-151. [Annotated archived copy]
Index entries for Colombian or self numbers and related sequences

Cf. A063018, A232485, A232487, A232488.

f:=proc(n) local t1,t2,i;
t1:=convert(n,base,10);
t2:=1;
for i from 1 to nops(t1) do if t1[i] <> 0 then t2:=t2*t1[i]; fi; od;
t2; end;
g:=n->n+f(n);
t1:=[3];
for n from 1 to 50 do t1:=[op(t1),g(t1[nops(t1)])]; od:
t1;

A030547 Number of terms (including the initial term) needed to reach a palindrome when the Reverse Then Add! map (x -> x + (x-with-digits-reversed)) is repeatedly applied to n, or -1 if a palindrome is never reached.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 2, 3, 2, 3, 3, 2, 2, 2, 2, 2, 1, 2, 3, 3, 4, 2, 2, 2, 2, 3, 2, 1, 3, 4, 5, 2, 2, 2, 3, 2, 3, 3, 1, 5, 7, 2, 2, 3, 2, 3, 3, 4, 5, 1, 25, 2, 3, 2, 3, 3, 4, 5, 7, 25

Offset: 1

Eric W. Weisstein

It is conjectured that a(196) is the smallest term equal to -1. See A023108.

Daniel Lignon, Dictionnaire de (presque) tous les nombres entiers, Ellipses, Paris, 2012, 702 pages. See Entry 196.

Eric Weisstein's World of Mathematics, 196 Algorithm.

Cf. A006960, A023108, A063018, etc.

Equals A033665(n) + 1.

Table[Length@
  NestWhileList[# + IntegerReverse[#] &, n, ! PalindromeQ[#]  &], {n, 98}] (* Robert Price, Oct 18 2019 *)

Edited by N. J. A. Sloane, May 09 2015

A383478 Number of lattice paths from (0,0) to (n,n) using steps (1,0),(2,0),(3,0),(0,1).

Original entry on oeis.org

1, 2, 9, 44, 220, 1134, 5950, 31608, 169488, 915420, 4972825, 27141036, 148711836, 817516196, 4506838380, 24906188912, 137933068572, 765324011736, 4253501563156, 23675286219200, 131955035141160, 736347621539310, 4113559552360230, 23003228298637080

Offset: 0

Seiichi Manyama, Apr 28 2025

nonn

Robert Israel, Table of n, a(n) for n = 0..1316

Main diagonal of A383477.

Cf. A063018.

f:= proc(x,y) option remember;
     local t;
     t:= 0;
     if x >= 1 then t:= t + procname(x-1,y) fi;
     if x >= 2 then t:= t + procname(x-2,y) fi;
     if x >= 3 then t:= t + procname(x-3,y) fi;
     if y >= 1 then t:= t + procname(x,y-1) fi;
     t
end proc:
f(0,0):= 1:
seq(f(n,n),n=0..25); # Robert Israel, May 28 2025

a(n) = [x^n] 1/(1 - x - x^2 - x^3)^(n+1).

a(n) = (n+1) * A063018(n+1).

cp's OEIS Frontend

A232486 a(1) = 3; thereafter a(n+1) = a(n) + product of nonzero digits of a(n).

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A030547 Number of terms (including the initial term) needed to reach a palindrome when the Reverse Then Add! map (x -> x + (x-with-digits-reversed)) is repeatedly applied to n, or -1 if a palindrome is never reached.

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A383478 Number of lattice paths from (0,0) to (n,n) using steps (1,0),(2,0),(3,0),(0,1).

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Maple

Formula