

A348624


a(n) = sum of row n of A348433 expressed as an irregular triangle.


1



31, 21, 2555, 2805, 3315, 17391, 38893, 104857575, 59363, 2097120, 31713, 376809, 117440484, 18790481885, 197132241, 2885681109, 42991575, 4966055899, 13153337295, 3959422917, 120946279055305, 4191888080835, 3729543441416139, 321057395310519, 84662395338675, 294669116243901
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

The binary expansion w of a(n) has an interesting appearance shown by the bitmap in links. We may divide w with length m into 3 parts: the most significant part includes all bits including the last 0 before the middle of the word, m/2, a central run of k 1's that includes all but the last 1 before a 0, and a least significant part that includes the last 1 in the central run of 1s and an assortment of 0's. For example, a(3) = 2555 > 100.11111.1011, which we may partition as shown by "." so as to preserve the otherwiseleading 0 in the last part. The central run of 1s generally increases in length as n increases.


LINKS



EXAMPLE

Table showing the first 5 rows of A348433 each having A348408(n) terms, and their sum a(n):
n\k 1 2 3 4 5 6 7 8 9 a(n) binary(a(n))

1: 1 2 4 8 16 > 31 > 11111
2: 7 14 > 21 > 10101
3: 5 10 20 40 80 160 320 640 1280 > 2555 > 100111111011
4: 11 22 44 88 176 352 704 1408 > 2805 > 101011110101
5: 13 26 52 104 208 416 832 1664 > 3315 > 110011110011


MATHEMATICA

c[1] = m = q = 1; Most@ Reap[Do[If[IntegerQ[c[#]], Set[n, 2 m], Set[n, #]] &@ Total@ IntegerDigits[m]; If[m > n, Sow[q]; Set[q, n], q += n]; Set[c[n], 1]; m = n, 650]][[1, 1]]
(* Extract up to 3961 terms from bitmap: *)
Block[{s = ImageData[ColorNegate@ Import["https://oeis.org/A348624/a348624_2.png"], "Bit"]}, Array[FromDigits[s[[#]], 2] &, 26]] (* Michael De Vlieger, Oct 26 2021 *)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



