A359841 Integers Xd which are divisible by X, where d is the last decimal digit.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420

Offset

1,1

Comments

Integers k such that k is divisible by A059995(k).

This sequence consists of {the thirty-two 2-digit terms of A034837 (from 10 up to 99)} Union {the positive multiples of 10 (A008592\{0})}.

Links

Table of n, a(n) for n=1..65.

N. N. Chentzov, D. O. Shklarsky, and I. M. Yaglom, The USSR Olympiad Problem Book, Selected Problems and Theorems of Elementary Mathematics, problem 15, pp. 11 and 102, Dover publications, Inc., New York, 1993.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Mathematica

Select[Range[10, 500], Divisible[#, Floor[#/10]] &] (* Amiram Eldar, Jan 15 2023 *)

Prog

(Python)
def ok(n): return n > 9 and n%(n//10) == 0
print([k for k in range(421) if ok(k)]) # Michael S. Branicky, Jan 15 2023
(Python)
def A359841(n): return (10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99)[n-1] if n <= 32 else (n-23)*10 # Chai Wah Wu, Jan 20 2023
(PARI) isok(k) = (k>9) && (k % (k \ 10) == 0); \\ Michel Marcus, Jan 20 2023

Crossrefs

Cf. A034837, A059995, A178157, A292683 (similar but with dX).

Subsequence: A008592\{0}.

Sequence in context: A038368 A062997 A110429 * A182363 A055982 A008717

Adjacent sequences: A359838 A359839 A359840 * A359842 A359843 A359844

Keyword

nonn,base,easy

Author

Bernard Schott, Jan 15 2023

Status

approved