A083553 Product of prime(n+1)-1 and prime(n)-1.

2, 8, 24, 60, 120, 192, 288, 396, 616, 840, 1080, 1440, 1680, 1932, 2392, 3016, 3480, 3960, 4620, 5040, 5616, 6396, 7216, 8448, 9600, 10200, 10812, 11448, 12096, 14112, 16380, 17680, 18768, 20424, 22200, 23400, 25272, 26892, 28552, 30616, 32040

Offset: 1

Author

Labos Elemer, May 22 2003

Keywords

• nonn

Comments

The conductor of x*prime(n) + y*prime(n+1); that is, for all k >= a(n), there exist nonnegative integers x and y such that k = x*prime(n) + y*prime(n+1). - T. D. Noe, Sep 22 2004

Examples

			n=25: a(25) = (97-1)*(101-1) = 9600.
		

References

• David Bressoud and Stan Wagon, A Course in Computational Number Theory, Key College Pub., 2000, p. 46.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A006093, A058263, A083538-A083555, A099407 (terms halved), A172042 [= A000010(a(n))], A256617.

One more than A037165.

Column 3 of A379010.

Programs

Mathematica

f[x_] := Prime[x]-1; Table[f[w+1]*f[w], {w, 1, 128}]

PARI

A083553(n) = ((prime(1+n)-1)*(prime(n)-1)); \\ Antti Karttunen, Dec 14 2024

Formula

a(n) = A006093(n+1)*A006093(n) = (prime(n+1)-1)*(prime(n)-1).

a(n) = A037165(n) + 1.

a(n) = 2*A099407(n). - Antti Karttunen, Dec 14 2024