A329804 Lexicographically earliest sequence of distinct positive integers such that the product a(n)*a(n+1) is "doubly true" (see the Comments section).

1, 2, 3, 10, 4, 16, 20, 5, 19, 30, 6, 21, 40, 7, 50, 8, 60, 9, 70, 11, 80, 12, 90, 13, 18, 38, 100, 14, 46, 105, 22, 61, 36, 103, 34, 106, 15, 93, 108, 25, 102, 35, 41, 29, 104, 26, 110, 17, 120, 23, 28, 109, 37, 130, 24, 72, 107, 43, 140, 27, 62, 31, 150, 32

Offset: 1

Author

Eric Angelini and Lars Blomberg, Nov 21 2019

Keywords

• base
• nonn
• look

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.

Examples

			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.
		

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.

Crossrefs

Cf. A007954, A252022 (same idea, but with doubly true additions).

Programs

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

Extensions

Edited by N. J. A. Sloane, Dec 09 2019