login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..55.

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

A133530, A133531, A133532, A133533, A160773

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 23 19:08 EST 2017. Contains 295128 sequences.