A344476 Decimal expansion of the value of the Buchstab function at phi + 2 = (5 + sqrt(5))/2 (A296184).

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

Offset: 0

Author

Amiram Eldar, May 20 2021

Keywords

• nonn
• cons

Examples

			0.56093863969277163346004116368055699296113179704964...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 286.

Links

• A. A. Bukhstab, Asymptotic estimates of a general number-theoretic function (in Russian), Matematicheskii Sbornik, Vol. 44, No. 6 (1937) pp. 1239-1246.
• Pieter Moree, A special value of Dickman's function, Math. Student, Vol. 64 (1995), pp. 47-50; entire volume.
• Eric Weisstein's World of Mathematics, Buchstab Function.
• Wikipedia, Buchstab function.

Crossrefs

Cf. A000796, A001622, A002390, A013661, A296184, A344475.

Programs

Mathematica

RealDigits[(1 + 2*Log[GoldenRatio] + Log[GoldenRatio]^2 - Pi^2/60)/(GoldenRatio + 2), 10, 100][[1]]

PARI

my(phi = quadgen(5)); (1 + 2*log(phi) + log(phi)^2 - Pi^2/60)/(phi+2) \\ Amiram Eldar, Jan 09 2025

Formula

Equals (1 + 2*log(phi) + log(phi)^2 - Pi^2/60)/(phi+2) (Moree, 1995).

Extensions

More terms from Amiram Eldar, Jan 09 2025