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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 (list; graph; refs; listen; history; text; internal format)
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)
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
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

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Last modified May 21 12:09 EDT 2024. Contains 372736 sequences. (Running on oeis4.)