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 = i-j and y=i*j; the list of the numbers x and y is then sorted into ascending order and duplicates are removed.

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

Offset

1,2

Comments

The first term is trivial since 0-0=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^(4n-1)+53*(10^(4n-1)-10^3)/101; if n=4k+3, a(n)=1161+483741*10^(4n-1)+159*(10^(4n-1)-10^3)/101. Note that the n-th term corresponds to that of the sequence, so the formulas are valid for n>3.

Example

For instance, 147*3=441 and 147-3=144 are terms; 161247387*3=483742161 and 161247387-3=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