A302191 Numerators of Hurwitz inverse of primes [2,3,5,7,...].

1, -3, 1, -5, -7, 97, -403, 3795, 1683, -67403, 141662, -5744835, -710829, 124489961, -7187558877, 247099181979, -43618981401, -2710990422171, 16455095049450, -1725616801459565, 2828334020055989, 58332444583336295, -2708485501761494555

Offset: 0

Author

N. J. A. Sloane and William F. Keigher, Apr 12 2018

Keywords

• sign
• frac

Comments

In the ring of Hurwitz sequences all members have offset 0.

Examples

			1/2, -3/4, 1, -5/8, -7/2, 97/4, -403/4, 3795/16, 1683/2, -67403/4, 141662, -5744835/8, -710829/2, 124489961/2, -7187558877/8, ...
		

References

• Xing Gao and William F. Keigher, Interlacing of Hurwitz series, Communications in Algebra, 45:5 (2017), 2163-2185, DOI: 10.1080/00927872.2016.1226885

Links

• N. J. A. Sloane, Maple programs for operations on Hurwitz sequences

Crossrefs

Cf. A302192, A302193.

Programs

Maple

# first load Maple commands for Hurwitz operations from link
s:=[seq(ithprime(n),n=1..64)];
Hinv(s);

Formula

E.g.f. for A302191/A302192 is 1 / Sum_{n >= 0} prime(n+1)*x^n/n!.