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.

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

1,1

Links

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

Example

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.

Prog

(PARI) 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

Crossrefs

Cf. A007954, A063108, A028842.

Sequence in context: A195613 A127652 A303812 * A259028 A358425 A317392

Adjacent sequences: A334531 A334532 A334533 * A334535 A334536 A334537

Keyword

nonn,base

Author

Scott R. Shannon, May 05 2020

Extensions

More terms from Giovanni Resta, May 07 2020

Status

approved