A063108 -id:A063108 - cp's OEIS frontend

A329725 a(1)=0, a(n) = n - (product of nonzero digits of n) - a(n-1).

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 1, 9, 1, 9, 1, 9, 1, 9, 1, 17, 2, 16, 1, 15, 0, 14, -1, 13, -2, 29, -1, 27, -3, 25, -5, 23, -7, 21, -9, 45, -8, 42, -11, 39, -14, 36, -17, 33, -20, 65, -19, 61, -23, 57, -27, 53, -31, 49, -35, 89, -34, 84, -39, 79, -44, 74, -49, 69, -54, 117

Offset: 1

Joshua Oliver, Nov 19 2019

a(10n+1)-a(10n-1)=1 for all positive integer n (conjectured).

			a(22) = 22 - 2*2 - 2 = 16.

Joshua Oliver, Table of n, a(n) for n = 1..5000

Cf. A063108, A063543.

R:= ListTools:-PartialSums(map(n -> (-1)^n*(n - convert(subs(0=NULL,convert(n,base,10)),`*`)), [$1..100])):
seq((-1)^n*R[n],n=1..100); # Robert Israel, Nov 20 2019

Nest[Append[#1, #2 - Last[#1] - Times @@ DeleteCases[IntegerDigits[#2], 0]] & @@ {#, Length@ # + 1} &, {0}, 69] (* Michael De Vlieger, Nov 19 2019 *)

for (n=1, 70, print1 (v=if (n==1, 0, n - vecprod(select(sign, digits(n))) - v)", ")) \\ Rémy Sigrist, Nov 28 2019

a(n) = Sum_{k=2..n} (-1)^(n-k)*A063543(k). - Robert Israel, Nov 20 2019

A334534 Numbers k such that (k-p)*(k+p) contains k as a substring, where p > 0 and p = A007954(k) is the product of digits of k.

Original entry on oeis.org

25, 28, 128, 225, 293, 678, 725, 742, 749, 4225, 4421, 6225, 8926, 72225, 617371, 1985525, 3679518, 4381824, 6816771, 8572645, 9721317, 43872768, 54639413, 758873243, 5895396725, 7796276839, 8881527332, 9458237492, 9594769255, 9949621217, 25214163187, 31987487294

Offset: 1

Scott R. Shannon, May 05 2020

			25 is a term as p = 2*5 = 10 and (25-10)*(25+10) = 525 which contains '25' as a substring.
8926 is a term as p = 8*9*2*6 = 864 and (8926-864)*(8926+864) = 78926980 which contains '8926' as a substring.

Giovanni Resta, Table of n, a(n) for n = 1..37 (terms < 3*10^12)

Cf. A007954, A063108, A028842.

isokp(dx, d) = {if (!#setintersect(Set(dx), Set(d)), return (0)); for (i=1, #dx - #d + 1, if (vector(#d, k, dx[k+i-1]) == d, return(1)););}
isokd(x, d, n) = {if (x==n, return (1)); my(dx = digits(x)); if (#dx < #d, return (0)); isokp(dx, d);}
isok(n) = {my(d = digits(n), p = vecprod(d)); if (p>0, isokd((n-p)*(n+p), d, n));} \\ Michel Marcus, May 07 2020

More terms from Giovanni Resta, May 07 2020

A095992 a(1) = 30; for n > 1, a(n+1) = a(n) + {product of nonzero digits of a(n)}.

Original entry on oeis.org

30, 33, 42, 50, 55, 80, 88, 152, 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, 4626, 4914, 5058, 5258, 5658

Offset: 1

Julien Piquet (julipiquet(AT)yahoo.fr), Jul 18 2004

From a puzzle; explanation found by Pierre Roger.

Frank Rubin, Number Series

Cf. A063108, A096347, A096972, A063108, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931, A096973, A096987.

a[1] = 30; a[n_] := a[n] = Block[{s = Sort[ IntegerDigits[a[n - 1]]]}, While[ s[[1]] == 0, s = Drop[s, 1]]; a[n - 1] + Times @@ s]; Table[ a[n], {n, 50}]
nxt[n_] := n+Times@@Select[IntegerDigits[n], #>0&]; NestList[nxt,30,50] (* Harvey P. Dale, Jan 08 2011 *)

The proposer suggests that this web site may contain other sequences also.

Edited and extended by Robert G. Wilson v and Klaus Brockhaus, Jul 20 2004

cp's OEIS Frontend

A329725 a(1)=0, a(n) = n - (product of nonzero digits of n) - a(n-1).

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A334534 Numbers k such that (k-p)*(k+p) contains k as a substring, where p > 0 and p = A007954(k) is the product of digits of k.

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A095992 a(1) = 30; for n > 1, a(n+1) = a(n) + {product of nonzero digits of a(n)}.

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