|
Search: id:A084951
|
|
|
| A084951 |
|
Primes in A075893: Primes of the form (p^2+q^2+r^2)/3, where p,q,r are 3 consecutive primes. |
|
+0
4
|
|
| 113, 193, 577, 1913, 2833, 10753, 44617, 48593, 54617, 69193, 74177, 78593, 86729, 102673, 107873, 122273, 156577, 183497, 214993, 228233, 247697, 308809, 334513, 414313, 581177, 602753, 617369, 636353, 691697, 861857, 1408993, 1786097
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
With the exception of 2^2+3^2+5^2=38 and 3^2+5^2+7^2=83 all sums of squares of 3 consecutive primes are divisible by 3 because mod(p^2,3)=1 for all primes p>3.
|
|
EXAMPLE
|
a(1)=113 because (7^2+11^2+13^2)/3=(49+121+169)/3=339/3=113 is prime.
|
|
MATHEMATICA
|
b = {}; a = 2; Do[k = (Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a)/3; If[PrimeQ[k], AppendTo[b, n]], {n, 1, 200}]; b - Artur Jasinski (grafix(AT)csl.pl), Sep 30 2007
|
|
CROSSREFS
|
Cf. A075893, A084952.
Cf. A133529, A133940.
Sequence in context: A142303 A152929 A142180 this_sequence A151947 A087703 A056710
Adjacent sequences: A084948 A084949 A084950 this_sequence A084952 A084953 A084954
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Hugo Pfoertner (hugo(AT)pfoertner.org), Jun 14 2003
|
|
EXTENSIONS
|
Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 30 2008 at the suggestion of R. J. Mathar.
|
|
|
Search completed in 0.002 seconds
|
