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A291463
a(n) is the product of n-th prime number with the distance to the next prime.
3
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
1,1
LINKS
FORMULA
a(n) = prime(n)*(prime(n+1) - prime(n)).
a(n) = A000040(n)*A001223(n). - Michel Marcus, Aug 25 2017
EXAMPLE
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.
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 *)
PROG
(PARI) forprime(p=2, 200, print1(p*nextprime(p+1)-p^2, ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Dimitris Valianatos, Aug 24 2017
STATUS
approved