OFFSET
1,2
COMMENTS
A "doubly true" product p*q has the property that the numerical product p*q is r and (the product of the digits of p) times (the product of the digits of q) is equal to the product of the digits of r.
As the sequence can always be extended with an integer ending in zero, it is infinite.
The sequence is a permutation of the positive integers.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..35000 (first 10000 terms from Lars Blomberg)
Rémy Sigrist, Scatterplot of the first 100000 terms.
Rémy Sigrist, Scatterplot of (n, a(n)-n) for n = 1..500000.
EXAMPLE
13*18 = 234 and (1*3)*(1*8) = 2*3*4
18*38 = 684 and (1*8)*(3*8) = 6*8*4
38*100 = 3800 and (3*8)*(1*0*0) = 3*8*0*0.
PROG
(PARI) dp(m) = vecprod(digits(m))
{ s=0; u=v=1; for (n=1, 64, print1 (v", "); s+=2^v; while (bittest(s, u), u++); for (w=u, oo, if (!bittest(s, w) && dp(v)*dp(w)==dp(v*w), v=w; break))) } \\ Rémy Sigrist, Nov 21 2019
CROSSREFS
KEYWORD
AUTHOR
Eric Angelini and Lars Blomberg, Nov 21 2019
EXTENSIONS
Edited by N. J. A. Sloane, Dec 09 2019
STATUS
approved