A130881 Numbers m such that digitsum((m+k)*abs(m-k)) = m for some k >= 0.

0, 1, 8, 9, 10, 17, 18, 26, 27, 35, 36, 44, 45, 53, 54, 62, 63, 71, 72, 80, 81, 89, 90, 98, 99, 107, 108, 116, 117, 125, 126, 134, 135, 143, 144, 152, 153, 161, 162, 170, 171, 179, 180, 188, 189, 197, 198, 206, 207, 215, 216, 224, 225, 233, 234, 242, 243, 251, 252

Offset

1,3

Comments

The sequence of first differences is eventually 2-periodic: 1, 7, 1, 1, 7, 1, 8, 1, 8, 1, 8, etc. The minimum numbers k associated with the first terms of the sequence are (m,k): (0,0), (1,0), (8,9), (9,0), (10,3), (17,24), (18,6), (26,75), etc.

Links

Table of n, a(n) for n=1..59.

Example

m = 27 -> k = 75 -> (27+75)*abs(27-75) = 102*48 = 4896 -> 4+8+9+6 = 27.

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+i)*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);

Crossrefs

Sequence in context: A070480 A135043 A054966 * A235399 A283628 A343860

Adjacent sequences: A130878 A130879 A130880 * A130882 A130883 A130884

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 26 2007

Status

approved