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

Author

Scott R. Shannon, May 05 2020

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

Cf. A007954, A063108, A028842.

Programs

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

Extensions

More terms from Giovanni Resta, May 07 2020