cp's OEIS Frontend

A267756 Indices of Euclid numbers (A006862) of the form x^2 + y^2 + z^2 where x, y and z are integers.

%I A267756 #13 Jan 30 2016 04:28:36
%S A267756 0,1,4,8,11,12,13,15,16,19,22,27,31,34,35,38,41,42,46,48,52,53,56,57,
%T A267756 61,62,64,65,66,69,70,71,73,74,76,77,78,79,80,83,84,86,87,88,89,91,93,
%U A267756 95,99,100,103,104,107,108,111,112,113,115,116,118,119,124,128,131,133
%N A267756 Indices of Euclid numbers (A006862) of the form x^2 + y^2 + z^2 where x, y and z are integers.
%C A267756 Corresponding Euclid numbers are 2, 3, 211, 9699691, 200560490131, 7420738134811, 304250263527211, 614889782588491411, 32589158477190044731, ...
%C A267756 Complement of this sequence is 2, 3, 5, 6, 7, 9, 10, 14, 17, 18, 20, 21, 23, 24, 25, 26, 28, 29, 30, 32, 33, 36, 37, 39, 40, 43, 44, 45, 47, 49, 50, 51, 54, 55, 58, 59, 60, 63, 67, 68, 72, 75, 81, 82, 85, 90, 92, 94, 96, 97, 98, 101, ...
%C A267756 Euclid numbers that are not of the form x^2 + y^2 + z^2 are 7, 31, 2311, 30031, 510511, 223092871, 6469693231, 13082761331670031, 1922760350154212639071, ...
%e A267756 0 is a term because A006862(0) = 2 = 0^2 + 1^2 + 1^2.
%e A267756 1 is a term because A006862(1) = 3 = 1^2 + 1^2 + 1^2.
%e A267756 4 is a term because A006862(4) = 211 = 3^2 + 9^2 + 11^2.
%e A267756 8 is a term because A006862(8) = 9699691 = 79^2 + 123^2 + 3111^2.
%o A267756 (PARI) isA004215(n) = { local(fouri, j) ; fouri=1 ; while( n >=7*fouri, if( n % fouri ==0, j= n/fouri -7 ; if( j % 8 ==0, return(1) ) ; ) ; fouri *= 4 ; ) ; return(0) ; }
%o A267756 a006862(n) = prod(k=1, n, prime(k))+1;
%o A267756 for(n=0, 200, if(!isA004215(a006862(n)), print1(n, ", ")));
%Y A267756 Cf. A004215, A006862.
%K A267756 nonn
%O A267756 1,3
%A A267756 _Altug Alkan_, Jan 20 2016