A370458 Partial products of A051179.

1, 3, 45, 11475, 752014125, 3229876072253041875, 59580697294650083747194059426068878125, 20274260698223485458204828871028994444941136941453077244297515184669623921875

Offset: 0

Author

Amiram Eldar, Feb 19 2024

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10
• Donald Knuth, Problem 11685, The American Mathematical Monthly, Vol. 120, No. 1 (2013), p. 76; The Reciprocal of the Thue-Morse Constant, Solution to Problem 11685 by Traian Viteam, ibid., Vol. 122, No. 1 (2015), pp. 81-82.
• Roberto Tauras, Problem 11685.

Crossrefs

Cf. A051179, A215016, A258714, A258715, A258716.

Programs

Mathematica

FoldList[Times, Table[2^(2^n) - 1, {n, 0, 7}]]

PARI

lista(nmax) = {my(v = 1); for(i = 0, nmax, v *= (2^(2^i) - 1); print1(v, ", "));}

Python

from math import prod
def A370458(n): return prod((1<<(1<Chai Wah Wu, Feb 19 2024

Formula

a(n) = Product_{k=0..n} A051179(k).

Sum_{n>=0} 1/a(n) = A258714 = 1/A215016 - 3/2 = 1.355642702854... (Knuth, 2013).