A296041 Decimal expansion of sqrt(1 + sqrt(3 + sqrt(6 + sqrt(10 + sqrt(15 + ... + sqrt(k*(k + 1)/2 + ...)))))).

1, 8, 6, 4, 4, 5, 8, 9, 5, 8, 1, 6, 3, 4, 8, 8, 1, 3, 2, 3, 5, 2, 0, 0, 3, 7, 1, 5, 2, 7, 3, 9, 4, 3, 7, 8, 4, 1, 5, 6, 4, 2, 2, 0, 6, 9, 8, 2, 6, 6, 4, 9, 9, 2, 3, 5, 8, 6, 9, 0, 4, 3, 8, 1, 8, 2, 7, 5, 3, 2, 5, 7, 3, 5, 8, 3, 4, 5, 5, 8, 1, 7, 7, 9, 9, 6, 4, 4, 9, 0, 6, 1, 9, 8, 3, 7, 8, 2, 2, 2

Offset

1,2

Links

Kelvin Voskuijl, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Nested Radical

Example

1.86445895816348813235200371527394378415642206982664...

Prog

(PARI) A296041_upto(N)=my(c); forstep(n=3*N\log(N)+3, 1, -1, c=sqrt(n*(n+1)/2+c)); digits(c*10^N\1) \\ M. F. Hasler, Apr 14 2026

Crossrefs

Cf. A000217, A072449, A099876, A099879, A105546, A105817, A239349, A257574, A257575, A257576, A257577, A257578.

Sequence in context: A388553 A388781 A388629 * A008569 A376883 A219863

Adjacent sequences: A296038 A296039 A296040 * A296042 A296043 A296044

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Dec 03 2017

Status

approved