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 A129541 Primes of the form p^2 + q^2 + A007918(p + q) - p - q, where p and q are consecutive primes. 0
 13, 37, 2333, 51229, 84131, 141539, 273821, 591893, 649813, 744221, 889877, 911269, 1065829, 2146619, 2205013, 2766007, 2913773, 3090187, 3348893, 3374821, 3505979, 3942493, 4095547, 4885981, 5766421, 6125029, 6336829 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The trial number was 80 pairs of consecutive primes to produce seven primes. Oddly it seems more productive as the pairs of primes increase in value, rather unusual for generators of primes. Perhaps an extension will confirm this. LINKS FORMULA For two consecutive primes p and q, add them and subtract that amount from the nearest prime greater than p+q. Call this number d; then see whether p^2 + q^2 + d is a prime. EXAMPLE Take consecutive primes 31 and 37. The sum 31 + 37 = 68 and is three less than the next prime 71. Hence 31^2 + 37^2 + 3 = 961+1369+3=2333 which is a prime that belongs to the sequence. MATHEMATICA cp[{a_, b_}]:=a^2+b^2+NextPrime[a+b]-a-b; Join[{13}, Select[cp/@ Partition[ Prime[Range], 2, 1], PrimeQ]] (* Harvey P. Dale, Nov 16 2013 *) PROG (PARI) p=2; forprime(q=3, 1e4, t=p^2+q^2+nextprime(p+q)-p-q; if(isprime(t), print1(t", ")); p=q) CROSSREFS Sequence in context: A262475 A309808 A201809 * A302858 A244185 A044090 Adjacent sequences: A129538 A129539 A129540 * A129542 A129543 A129544 KEYWORD nonn AUTHOR J. M. Bergot, Jun 08 2007 EXTENSIONS Extended, edited, and program added by Charles R Greathouse IV, Nov 11 2009 STATUS approved

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Last modified January 27 02:34 EST 2023. Contains 359836 sequences. (Running on oeis4.)