A225359 Decimal expansion of suggested value for N_eff: the effective number of neutrino species present in the era before recombination.

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

Offset

1,1

Comments

Decimal expansion of (3 + (4/7)*(43/57)^(4/3) = 3 + 172*(43/57)^(1/3)/399).

Steven Weinberg suggested that the contribution from Goldstone bosons to the effective number of neutrino species present in the era before recombination would be (4/7)*(43/57)^(4/3) = 0.392422..., so N_eff should be 3 + (4/7)*(43/57)^(4/3) = 3.392422...

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Steven Weinberg, Goldstone bosons as fractional cosmic neutrinos, Physical Review Letters, Vol. 110, No. 24 (2013), Article 241301; arXiv preprint, arXiv:1305.1971 [astro-ph.CO], 2013.

Wikipedia, Neutrino.

Index entries for algebraic numbers, degree 3.

Formula

Equals 3 + (4/7)*(43/57)^(4/3) = 3 + A225357.

Minimal polynomial: 3620708343*x^3 - 32586375087*x^2 + 97759125261*x - 97977928525. - Amiram Eldar, Apr 22 2026

Example

3.39242206416083273234087942036126444137824088551113392562848...

Mathematica

First[RealDigits[3 + 4*(43/57)^(4/3)/7, 10, 100]] (* Paolo Xausa, Apr 22 2026 *)

Crossrefs

Cf. A225357.

Sequence in context: A070517 A290408 A028232 * A060310 A093096 A097670

Adjacent sequences: A225356 A225357 A225358 * A225360 A225361 A225362

Keyword

nonn,cons,easy

Author

Omar E. Pol, May 28 2013

Status

approved