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

Author

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

Keywords

• nonn
• base

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]

Crossrefs

Cf. A054986, A178158.

A subsequence of A067251, disjoint with A034709.

Programs

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

PARI

is_nm( x )=x%10 && x%(x%10)==x\10^(#Str(x)-1)
for(n=1,999,is_nm(n)&print1(n","))

Formula

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

Extensions

Edited by M. F. Hasler, Jan 14 2014