A291463 a(n) is the product of n-th prime number with the distance to the next prime.

2, 6, 10, 28, 22, 52, 34, 76, 138, 58, 186, 148, 82, 172, 282, 318, 118, 366, 268, 142, 438, 316, 498, 712, 388, 202, 412, 214, 436, 1582, 508, 786, 274, 1390, 298, 906, 942, 652, 1002, 1038, 358, 1810, 382, 772, 394, 2388, 2532, 892, 454, 916, 1398, 478, 2410

Offset: 1

Author

Dimitris Valianatos, Aug 24 2017

Keywords

• nonn

Examples

			For n = 6 prime(6) = 13, prime(7) = 17 the gap is 17 - 13 = 4. So 13 * 4 = 52 and 52 is the sixth term.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001223, A048852.

Programs

Mathematica

Array[With[{p = Prime@ #}, p (NextPrime[p] - p)] &, 50] (* Michael De Vlieger, Sep 03 2017 *)
Module[{nn=60,dnp},dnp=Differences[Prime[Range[nn+1]]];Times@@@Thread[ {Prime[Range[nn]],dnp}]] (* Harvey P. Dale, Mar 24 2022 *)

PARI

forprime(p=2,200, print1(p*nextprime(p+1)-p^2, ", "))

Formula

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

a(n) = A000040(n)*A001223(n). - Michel Marcus, Aug 25 2017