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A273909 Let p = prime(n) and q = prime(n+1), then a(n) = p*q - p^2 - 2*q. 0
-4, -4, -4, 6, -4, 18, -4, 30, 80, -4, 112, 66, -4, 78, 176, 200, -4, 232, 126, -4, 280, 150, 320, 518, 186, -4, 198, -4, 210, 1328, 246, 512, -4, 1092, -4, 592, 616, 318, 656, 680, -4, 1428, -4, 378, -4, 1966, 2086, 438, -4, 450 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = -4 only when prime(n) is the smaller of a twin prime pair or prime(1) = 2 where a(1) = 2*3-2^2-2*3 = -4.

Let g be the gap between prime(n) and prime(n + 1) i.e. g = q - p. Then a(n) = (g - 2) * p - 2 * g = (A001223(n) - 2) * A000040(n) - 2 * A001223(n). - David A. Corneth, Jun 06 2016

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

For n=5, p = prime(5) = 11, q = prime(6) = 13, a(5) = 11*13-11^2-2*13 = -4.

For n=6, p = prime(6) = 13, q = prime(7) = 17, a(6) = 13*17-13^2-2*17 = 18.

MATHEMATICA

Table[Prime@ n Prime[n + 1] - Prime[n]^2 - 2 Prime[n + 1], {n, 54}] (* Michael De Vlieger, Jun 04 2016 *)

PROG

(PARI) forprime(p=1, 300, q=nextprime(p+1); print1(p*q-p^2-2*q, ", "))

(PARI) p=2; forprime(q=3, 1e3, print1(p*(q-p)-2*q", "); p=q) \\ Charles R Greathouse IV, Jun 10 2016

CROSSREFS

Sequence in context: A140696 A160401 A114742 * A098013 A073229 A116446

Adjacent sequences:  A273906 A273907 A273908 * A273910 A273911 A273912

KEYWORD

sign

AUTHOR

Dimitris Valianatos, Jun 03 2016

STATUS

approved

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Last modified July 31 04:27 EDT 2021. Contains 346367 sequences. (Running on oeis4.)