A210582 Numbers whose first digit is the remainder of their division by the last digit (in base 10).

13, 19, 23, 26, 29, 39, 46, 49, 59, 69, 79, 89, 103, 109, 127, 133, 163, 193, 197, 199, 203, 206, 209, 214, 218, 233, 234, 236, 247, 254, 258, 263, 266, 274, 293, 294, 296, 298, 299, 309, 367, 399, 406, 409, 417, 428, 436, 466, 468, 487, 496, 499, 509, 537, 599, 609, 638, 657, 678, 699, 709, 799, 809, 899

Offset

1,1

Comments

This is a restricted or simplified version of the definition of modest numbers A054986.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

E. Angelini, Not Modest, Mar 22 2012

E. Angelini, Not modest [Cached copy, with permission]

Formula

a(n) mod A010879(a(n)) = A000030(a(n)). [Reinhard Zumkeller, Mar 26 2011]

Prog

(PARI) is_nm( x )=x%10 && x%(x%10)==x\10^(#Str(x)-1)
for(n=1, 999, is_nm(n)&print1(n", "))
(Haskell)
a210582 n = a210582_list !! (n-1)
a210582_list = filter (\x -> mod x (a010879 x) == a000030 x) a067251_list
-- Reinhard Zumkeller, Mar 26 2012
(Magma) [ n: n in [1..1002] | not IsZero(d[1]) and n mod d[1] eq d[#d] where d is Intseq(n) ];  // Bruno Berselli, Mar 26 2012

Crossrefs

Cf. A054986, A178158.

A subsequence of A067251, disjoint with A034709.

Sequence in context: A088184 A274407 A054986 * A071621 A240565 A160951

Adjacent sequences: A210579 A210580 A210581 * A210583 A210584 A210585

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Mar 22 2012

Extensions

Edited by M. F. Hasler, Jan 14 2014

Status

approved