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

Author

Stefano Spezia, Jul 22 2021

Keywords

• nonn
• base

Comments

Union of 100*A000027, A053742, A324297 and A346507.

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.

Crossrefs

Cf. A000027, A053742, A324297, A346507.

Programs

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

PARI

isok(k) = my(u=k%10); sumdiv(k, d, (d>1) && (d 0; \\ Michel Marcus, Jul 23 2021

Formula

Lim_{n->infinity} a(n)/a(n-1) = 1.