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

1,2

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

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

Sequence in context: A306465 A276104 A376370 * A274299 A119023 A213962

Adjacent sequences: A329801 A329802 A329803 * A329805 A329806 A329807

Keyword

base,nonn,look

Author

Eric Angelini and Lars Blomberg, Nov 21 2019

Extensions

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

Status

approved