A344475 Decimal expansion of the value of the Dickman function at phi + 1 = phi^2 = (3 + sqrt(5))/2 (A104457).

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

Offset

0,3

References

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

Links

Table of n, a(n) for n=0..104.

Pieter Moree, A special value of Dickman's function, Math. Student, Vol. 64 (1995), pp. 47-50; entire volume.

Pieter Moree, Nicolaas Govert de Bruijn, the enchanter of friable integers, Indagationes Mathematicae, Vol. 24, No. 4 (2013), pp. 774-801.

Eric Weisstein's World of Mathematics, Dickman Function.

Wikipedia, Dickman function.

Formula

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

Example

0.10464776377316485385416972771819339482414269115729...

Mathematica

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

Prog

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

Crossrefs

Cf. A000796, A001622, A002390, A013661, A104457, A344476.

Cf. A175475, A244009 (value at 1/2), A245238, A309638.

Sequence in context: A181110 A199959 A084892 * A245556 A256318 A018835

Adjacent sequences: A344472 A344473 A344474 * A344476 A344477 A344478

Keyword

nonn,cons,changed

Author

Amiram Eldar, May 20 2021

Extensions

More terms from Amiram Eldar, Jan 09 2025

Status

approved