

A329804


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


4



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
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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: A031275 A306465 A276104 * 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



