A098780 First n numbers in binary representation concatenated in reverse order.

1, 5, 29, 157, 1437, 13725, 128413, 1176989, 20051357, 355595677, 6261175709, 109340390813, 1896046785949, 32682372363677, 560447953696157, 9567647208437149, 315812421869630877, 10692105963331253661

Offset

1,2

Links

Indranil Ghosh, Table of n, a(n) for n = 1..412

Index entries for sequences related to Most Wanted Primes video

Formula

a(n) = n*A000079(A070939(a(n-1))) + a(n-1); a(1) = 1.

a(n) = n*2^(1 + floor(log_2(a(n-1)))) + a(n-1); a(1) = 1.

Example

a(4) = (4 3 2 1) -> (100 11 10 1) -> 10011101 -> 157.

Mathematica

Table[FromDigits[Flatten[IntegerDigits[#, 2]&/@Reverse[Range[n]]], 2], {n, 20}] (* Harvey P. Dale, Sep 10 2019 *)

Prog

(Python)
def A098780(n):
....s=""
....for i in range(n, 0, -1):
........s+=bin(i)[2:]
....return int(s, 2) # Indranil Ghosh, Jan 28 2017
(Python)
from functools import reduce
def A098780(n): return reduce(lambda i, j:(i<<j.bit_length())+j, range(n, 0, -1)) # Chai Wah Wu, Feb 26 2023

Crossrefs

Cf. A007088, A047778.

Sequence in context: A320089 A239715 A260752 * A222700 A272940 A146178

Adjacent sequences: A098777 A098778 A098779 * A098781 A098782 A098783

Keyword

nonn,base

Author

Reinhard Zumkeller, Oct 04 2004

Extensions

Typo in data corrected by D. S. McNeil, Aug 20 2010

Status

approved