A255765 Partial sums of A255744.

1, 11, 21, 111, 121, 211, 301, 1111, 1121, 1211, 1301, 2111, 2201, 3011, 3821, 11111, 11121, 11211, 11301, 12111, 12201, 13011, 13821, 21111, 21201, 22011, 22821, 30111, 30921, 38211, 45501, 111111, 111121, 111211, 111301, 112111, 112201, 113011, 113821, 121111

Offset

1,2

Comments

Also, this is a row of the square array A255741.

Is this sequence related to positive repunits? (see formula section).

Links

Felix Fröhlich, Table of n, a(n) for n = 1..10000

Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 33.

Formula

Question: a(2^k) = A002275(k+1), k >= 0. Is this true?

Mathematica

Accumulate@ MapAt[Floor, Array[10*9^(DigitCount[# - 1, 2, 1] - 1) &, 40], 1] (* Michael De Vlieger, Nov 03 2022 *)

Prog

(PARI) lista(nn) = {s = 1; for (n=2, nn, print1(s, ", "); s += 10*9^(hammingweight(n-1)-1); ); } \\ Michel Marcus, Mar 15 2015
(PARI) a(n) = sum(k=1, n, if (k==1, 1, 10*9^(hammingweight(k-1)-1))); \\ Michel Marcus, Mar 15 2015

Crossrefs

Cf. A002275, A005408, A151788, A147562, A151790, A151781, A151792, A151793, A255740, A255741, A255744, A255764, A255766.

Sequence in context: A058489 A278780 A071158 * A071157 A096104 A126299

Adjacent sequences: A255762 A255763 A255764 * A255766 A255767 A255768

Keyword

nonn

Author

Omar E. Pol, Mar 05 2015

Extensions

More terms from Michel Marcus, Mar 15 2015

Status

approved