A143682 a(n) = (prime(n)^4 - prime(n^4))/2, where prime(n) is the n-th prime.

7, 14, 103, 391, 5002, 8967, 31065, 45724, 107077, 301276, 382000, 820141, 1246909, 1479730, 2129740, 3534420, 5523879, 6237871, 9209731, 11625564, 12865129, 17844972, 21754756, 28999632, 41437737, 48684207, 52341667, 60941856

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 01 2008

Keywords

• nonn

Examples

			a(1) = (prime(1)^2^2 - prime(1^2^2))/2 = (16 - 2)/2 = 14/2 = 7,
a(2) = (prime(2)^2^2 - prime(2^2^2))/2 = (81 - 53)/2 = 28/2 = 14,
a(3) = (prime(3)^2^2 - prime(3^2^2))/2 = (625 - 419)/2 = 206/2 = 103,
a(4) = (prime(4)^2^2 - prime(4^2^2))/2 = (2401 - 1619)/2 = 782/2 = 391 = a(4),
a(5) = (prime(5)^2^2 - prime(5^2^2))/2 = (14641 - 4637)/2 = 10004/2 = 5002,
etc.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..750

Crossrefs

Cf. A000040.

Cf. A030514, A109791. - R. J. Mathar, Nov 05 2008

Programs

Magma

[(NthPrime(n)^4 - NthPrime(n^4))/2: n in [1..30]]; // Vincenzo Librandi, Oct 05 2015

Maple

A143682 := proc(n) (ithprime(n)^4-ithprime(n^4))/2 ; end: for n from 1 to 50 do printf("%d,",A143682(n)) ; od: # R. J. Mathar, Nov 05 2008

Mathematica

Table[(Prime[n]^4 - Prime[n^4])/2, {n, 40}] (* G. C. Greubel, May 29 2021 *)

PARI

a(n) = (prime(n)^4 - prime(n^4))/2; \\ Michel Marcus, Oct 05 2015

Sage

[(nth_prime(n)^4 - nth_prime(n^4))/2 for n in (1..40)] # G. C. Greubel, May 29 2021

Extensions

More terms from R. J. Mathar, Nov 05 2008