A248050 Lexicographically earliest increasing sequence such that a(n) equals the sum of digits of the terms up to and including a(n).

0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 198, 207, 216, 225, 234, 243, 252, 261, 279, 297, 306, 315, 324, 333, 342, 351, 360, 378, 396, 405, 414, 423, 432, 441, 459, 477, 495, 504, 513, 522, 531, 540, 558, 576, 594, 603, 612, 621, 639, 657, 675, 693, 702, 711, 720, 738, 756, 774, 792

Offset

0,2

Comments

The offset could equally well be chosen to be 1, but taking it equal to zero allows us to consider {a(n); n=0,1,2...} and {a(n); n=1,2...} together, both of which satisfy the definition.

All terms are divisible by 9, but there is no limit on the size of the gaps. The first gap of 18 occurs after a(9)=81 followed by a(10)=99, the first gap of 27 after a(79)=972 followed by a(80)=999.

There seems also to be no limit on the "look-ahead" required to avoid getting stuck by a bad choice.

Links

M. F. Hasler, Table of n, a(n) for n = 0..1000

E. Angelini, Cumulative sum of the digits used so far, SeqFan mailing list, Oct 30 2014

Prog

(PARI) a(n, a=0, L=19)={local(ok(n, L)=!L||for(k=1, #Str(n), sumdigits(n+=9)/9==k&&ok(n, L-1)&&return(n))); for(i=1, n, print1(s=a", "); until(s+sumdigits(a+=9)==a&&ok(a, L), )); a}

Crossrefs

Sequence in context: A052223 A085132 A111708 * A044052 A131418 A249605

Adjacent sequences: A248047 A248048 A248049 * A248051 A248052 A248053

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Oct 30 2014

Status

approved