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

Author

Reinhard Zumkeller, Oct 04 2004

Keywords

• nonn
• base

Examples

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

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..412
• Index entries for sequences related to Most Wanted Primes video

Crossrefs

Cf. A007088, A047778.

Programs

Mathematica

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

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<Chai Wah Wu, Feb 26 2023

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.

Extensions

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