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 A176613 Smallest prime p of three consecutive primes such that the sum of their n-th powers is prime, or 0 if such a prime does not exist. 0
 2, 5, 3, 23, 0, 11, 0, 5, 0, 23, 3, 137, 0, 5, 3, 89, 0, 71, 0, 17, 0, 23, 0, 23, 3, 131, 3, 419, 0, 31, 0, 859, 0, 31, 0, 127, 0, 11, 0, 359, 0, 31, 0, 347, 0, 509, 0, 137, 0, 193, 0, 769, 0, 23, 0, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Let p = prime(i), q = prime(i+1), r = prime(i+2). (*) p^n + q^n + r^n has to be a prime. When n is even and p > 3, then (*) is composite because primes greater than 3 are either of form 6k-1 or 6k+1 for some k. Hence, squares (or any even power) of such a prime has the form 6k+1. Adding three such even powers will produce a number of the form 6k+3, which is divisible by 3. When n is even and p = 3, sequence A160773 gives the even n for which 3^n + 5^n + 7^n is prime. LINKS EXAMPLE 5 + 7 + 11 = 23 = prime(9); 3^2 + 5^2 + 7^2 = 83 = prime(23); 23^3 + 29^3 + 31^3 = 66347 = prime(6616). CROSSREFS Sequence in context: A077216 A227617 A058357 * A097754 A122992 A051497 Adjacent sequences:  A176610 A176611 A176612 * A176614 A176615 A176616 KEYWORD nonn AUTHOR Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 21 2010 EXTENSIONS a(0) term added by T. D. Noe, Nov 23 2010 STATUS approved

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