

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



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


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STATUS

approved



