Dr. Michael W. Ecker - cp's OEIS frontend

User: Dr. Michael W. Ecker

Dr. Michael W. Ecker has authored 1 sequences.

A328918 a(n) is the number of ordered pairs of positive integers (x, y) with x + y = 10^n, where x and y each have exactly n-digits but with initial zero digits allowed, and as strings, x and y are permutations of each other.

1, 1, 11, 11, 281, 281, 11181, 11181, 563131, 563131, 32795191, 32795191, 2103687091, 2103687091, 144420919291, 144420919291, 10421915468041, 10421915468041, 781300466839541, 781300466839541, 60358948031151561, 60358948031151561, 4777791013174712961

Offset: 1

Dr. Michael W. Ecker, Oct 30 2019

Published with slightly different wording in Mathematics Magazine, Problem 1016, Dec. 1977.
Analyzed for n = 1, 2, 3; computer-verified for n up to 8.
All solutions consist of an even number of digits followed by the digit 5 followed by zero or more 0's. This pattern means that a(2*n-1) = a(2*n). The initial segment consists of pairs of digits that add to 9 (0 with 9, 1 with 8, etc) arranged in arbitrary order and in particular leading 0's are permitted by the definition of the problem. A287317(k) gives the number of such arrangement with k pairs. For example, 339606500 + 660393500 is a solution. - Andrew Howroyd, Nov 03 2019

			For n = 3, solutions are (095, 905), (185, 815), (275, 725), (365, 635), (455, 545), (500, 500), (545, 455), (635, 365), (725, 275), (815, 185), (905, 095).

Michael W. Ecker, Problem 1016, Mathematics Magazine, Vol. 50, No. 3 (May, 1977), pp. 163-169.

Cf. A287317.

seq(n)={Vec(serlaplace(besseli(0,2*x + O(x*x^n))^5)/(1-x))} \\ Andrew Howroyd, Nov 03 2019

a(n) = Sum_{k=0..floor((n-1)/2)} A287317(k). - Andrew Howroyd, Nov 03 2019

Terms a(9) and beyond from Andrew Howroyd, Nov 03 2019

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User: Dr. Michael W. Ecker

A328918 a(n) is the number of ordered pairs of positive integers (x, y) with x + y = 10^n, where x and y each have exactly n-digits but with initial zero digits allowed, and as strings, x and y are permutations of each other.

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