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A255765
Partial sums of A255744.
5
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
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Mar 05 2015
EXTENSIONS
More terms from Michel Marcus, Mar 15 2015
STATUS
approved