

A322905


Sequence consists of all pairs of numbers x and y such that x is the reverse of y, and there exist numbers i and j such that x = ij and y=i*j; the list of the numbers x and y is then sorted into ascending order and duplicates are removed.


0



0, 144, 441, 1475244, 4425741, 161247384, 483742161, 14752475244, 44257425741, 1612475247384, 4837425742161, 147524752475244, 442574257425741, 16124752475247384, 48374257425742161
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OFFSET

1,2


COMMENTS

The first term is trivial since 00=0*0=0. The pattern of 147 followed by blocks of 5247 followed by 5244 (and its reverse) continues indefinitely. This is also true for the pattern of 161247 followed by blocks of 5247 followed by 384 (and its reverse).


LINKS

Table of n, a(n) for n=1..15.
W. P. Lo and Y. Paz, On finding all positive integers a,b such that b±a and ab are palindromic, arXiv:1812.08807 [math.HO] (2018).


FORMULA

For some positive integer k, if n=4k, a(n)=3+147*10^(4n)+53*(10^(4n)1)/101; if n=4k+1, a(n)=441*10^(4n)+159*(10^(4n)1)/101; if n=4k+2, a(n)=384+161247*10^(4n1)+53*(10^(4n1)10^3)/101; if n=4k+3, a(n)=1161+483741*10^(4n1)+159*(10^(4n1)10^3)/101. Note that the nth term corresponds to that of the sequence, so the formulas are valid for n>3.


EXAMPLE

For instance, 147*3=441 and 1473=144 are terms; 161247387*3=483742161 and 1612473873=161247384 are terms too.


MATHEMATICA

Do[If[IntegerDigits[x y] == Reverse[IntegerDigits[y  x]], Print[{x, y, y  x, x y}]], {x, 0, 10}, {y, x, 100000000}]


CROSSREFS

Cf. A004086, A166749 (sum and product of two integers).
Sequence in context: A188246 A258382 A151820 * A281240 A014770 A131528
Adjacent sequences: A322902 A322903 A322904 * A322906 A322907 A322908


KEYWORD

nonn,easy,base


AUTHOR

Wang Pok Lo, Dec 30 2018


STATUS

approved



