A064819 a(n) = p(1)*p(2)*...*p(n) - p(n+1)^2, where p(i) = i-th prime.

-7, -19, -19, 89, 2141, 29741, 510149, 9699161, 223092029, 6469692269, 200560488761, 7420738133129, 304250263525361, 13082761331667821, 614889782588488601, 32589158477190041249, 1922760350154212635349, 117288381359406970978781

Offset

1,1

Comments

It is known that a(n) > 0 for n >= 4.

References

R. Honsberger, Mathematical Diamonds, MAA, 2003, see p. 79. [Added by N. J. A. Sloane, Jul 05 2009]

H. Rademacher & O. Toeplitz, The Enjoyment of Mathematics, pp. 187-192 Dover NY 1990.

J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939.

Links

Harry J. Smith, Table of n, a(n) for n = 1..100

S. Bulman-Fleming and E. T. H. Wang, Problem 356, College Math. J., 20 (1989), 265.

Wikipedia, Bonse's inequality

Prog

(PARI) { p=1; for (n=1, 100, p*=prime(n); write("b064819.txt", n, " ", p - prime(n + 1)^2) ) } \\ Harry J. Smith, Sep 27 2009
(PARI) a(n) = prod(k=1, n, prime(k)) - prime(n+1)^2; \\ Michel Marcus, Jun 19 2018
(Python)
from sympy import prime, primorial
def A064819(n): return primorial(n)-prime(n+1)**2 # Chai Wah Wu, Feb 24 2023

Crossrefs

Cf. A135734, A060882, A062234.

Sequence in context: A195867 A344711 A052256 * A281915 A102167 A214525

Adjacent sequences: A064816 A064817 A064818 * A064820 A064821 A064822

Keyword

sign

Author

N. J. A. Sloane, Oct 23 2001

Status

approved