A346526 Positive integers k that are the product of two integers greater than 1 and ending with the same digit as k.
25, 36, 75, 96, 100, 121, 125, 156, 175, 200, 216, 225, 231, 256, 275, 276, 300, 325, 336, 341, 375, 396, 400, 416, 425, 441, 451, 456, 475, 500, 516, 525, 561, 575, 576, 600, 625, 636, 651, 671, 675, 676, 696, 700, 725, 736, 756, 775, 781, 800, 816, 825, 861, 875
Offset: 1
Examples
25 = 5*5, 36 = 6*6, 75 = 5*15, 96 = 6*16, 100 = 10*10, 121 = 11*11, 125 = 5*25, 156 = 6*26, 175 = 5*35, 200 = 10*20, 216 = 6*36, 225 = 15*15, 231 = 11*21, ...
Links
- Fung Cheok Yin, Limit of the ratio of a(n) to a(n-1) in A346526, Aug 12 2021.
Programs
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Lisp
(setf candidates (list 25)) (setf result nil) (defun factor (num small-num) (equalp 0 (mod num small-num))) (defun same-end-digit (num1 num2 num3) (and (equalp (mod num1 10) (mod num2 10)) (equalp (mod num2 10) (mod num3 10)))) (defun good-factor-p (num) (loop for i from 5 to (sqrt num) do ( if (factor num i) ( if (same-end-digit num i (/ num i) ) (return T) )))) (loop for i from 26 to 9000 do ( if (or (equalp 0 (mod i 10)) (equalp 1 (mod i 10)) (equalp 5 (mod i 10)) (equalp 6 (mod i 10))) (push i candidates))) (dolist (element candidates) (if (good-factor-p element) (push element result))) (format t (write-to-string result)) \\ FUNG Cheok Yin, Aug 12 2021
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PARI
isok(k) = my(u=k%10); sumdiv(k, d, (d>1) && (d
Formula
Lim_{n->infinity} a(n)/a(n-1) = 1.
Comments