A120740 Numbers n such that n = Sum_digits[k*abs(n-k)] for some k>=0.

0, 4, 5, 9, 14, 18, 23, 27, 32, 36, 41, 45, 50, 54, 59, 63, 68, 72, 77, 81, 86, 90, 95, 99, 104, 108, 113, 117, 122, 126, 131, 135, 140, 144, 149, 153, 158, 162, 167, 171, 176, 180, 185, 189, 194, 198, 203, 207, 212, 216, 221, 225, 230, 234, 239, 243, 248, 252

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 26 2007

Keywords

• nonn
• base

Comments

The first difference is eventually 2-periodic: 4, 1, 4, 5, 4, 5, 4, etc. The minimum numbers k associated to the first elements of the sequence are (n,k): (0,0), (4,2), (5,7), (9,3), (14,19), (18,33), (23,67), (27,69), etc.

Examples

			n = 36 -> k = 279 -> 279*abs(36-279)=279*243=67797 -> 6+7+7+9+7 = 36
		

Crossrefs

Cf. A130877.

Programs

Maple

P:=proc(n) local i, j, k, w; for i from 0 by 1 to n do for j from 0 by 1 to 100*n do w:=0; k:=j*abs(i-j); while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if w=i then print(i); break; fi; od; od; end: P(100000);

Formula

Conjecture: a(n) = (18*n-(-1)^n-35)/4 for n>2. a(n) = a(n-1)+a(n-2)-a(n-3) for n>5. G.f.: x^2*(4+x+4*x^3)/((1-x)^2*(1+x)). [Colin Barker, Apr 10 2012]