A102719 a(n) = a(n-1) + (sum of the last three digits of the sequence so far); a(0)=0; a(1)=1; a(2)=2 and a(n) < a(n+1).

0, 1, 2, 5, 13, 22, 29, 42, 57, 71, 86, 101, 103, 107, 115, 122, 127, 137, 148, 161, 169, 185, 199, 218, 229, 242, 250, 257, 271, 281, 292, 305, 313, 320, 325, 335, 346, 359, 376, 392, 406, 416, 427, 440, 448, 464, 478, 497, 517, 530, 538, 554, 568, 587, 607

Offset: 0

Author

Eric Angelini, Feb 06 2005

Keywords

• base
• easy
• nonn

Examples

			86+(1+8+6) = 101.
101+(1+0+1) = 103.
103+(1+0+3) = 107.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A102039.

Programs

Maple

a:= proc(n) option remember; local k, i; if n<2 then n elif n=2 then b(2):= [2,1,0]; 2 else k:= a(n-1) +add (i, i=b(n-1)); b(n):= [convert (k, base, 10)[], b(n-1)[]][1..3]; k fi end: seq (a(n), n=0..80); # Alois P. Heinz, Aug 13 2009

Mathematica

nxt[{a_,b_,c_}]:={b,c,c+Total[Take[Flatten[Join[IntegerDigits[a],IntegerDigits[b],IntegerDigits[c]]],-3]]}; NestList[nxt,{0,1,2},60][[;;,1]] (* Harvey P. Dale, Mar 13 2025 *)

Extensions

Corrected and extended by Alois P. Heinz, Aug 13 2009