A329804 - OEIS

%I #23 Nov 05 2023 21:28:49

%S 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,

%T 100,14,46,105,22,61,36,103,34,106,15,93,108,25,102,35,41,29,104,26,

%U 110,17,120,23,28,109,37,130,24,72,107,43,140,27,62,31,150,32

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

%C 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.

%C As the sequence can always be extended with an integer ending in zero, it is infinite.

%C The sequence is a permutation of the positive integers.

%H N. J. A. Sloane, <a href="/A329804/b329804.txt">Table of n, a(n) for n = 1..35000</a> (first 10000 terms from Lars Blomberg)

%H Rémy Sigrist, <a href="/A329804/a329804.png">Scatterplot of the first 100000 terms</a>.

%H Rémy Sigrist, <a href="/A329804/a329804_1.png">Scatterplot of (n, a(n)-n) for n = 1..500000</a>.

%e 13*18 = 234 and (1*3)*(1*8) = 2*3*4

%e 18*38 = 684 and (1*8)*(3*8) = 6*8*4

%e 38*100 = 3800 and (3*8)*(1*0*0) = 3*8*0*0.

%o (PARI) dp(m) = vecprod(digits(m))

%o { 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

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

%K base,nonn,look

%O 1,2

%A _Eric Angelini_ and _Lars Blomberg_, Nov 21 2019

%E Edited by _N. J. A. Sloane_, Dec 09 2019