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

1,1

Comments

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

Links

Table of n, a(n) for n=1..54.

Fung Cheok Yin, Limit of the ratio of a(n) to a(n-1) in A346526, Aug 12 2021.

Formula

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

Example

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, ...

Prog

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

Crossrefs

Cf. A000027, A053742, A324297, A346507.

Sequence in context: A263095 A077502 A297415 * A282550 A265505 A162305

Adjacent sequences: A346523 A346524 A346525 * A346527 A346528 A346529

Keyword

nonn,base

Author

Stefano Spezia, Jul 22 2021

Status

approved