%I #13 Jan 30 2016 04:28:36
%S 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 61,62,64,65,66,69,70,71,73,74,76,77,78,79,80,83,84,86,87,88,89,91,93,
%U 95,99,100,103,104,107,108,111,112,113,115,116,118,119,124,128,131,133
%N Indices of Euclid numbers (A006862) of the form x^2 + y^2 + z^2 where x, y and z are integers.
%C Corresponding Euclid numbers are 2, 3, 211, 9699691, 200560490131, 7420738134811, 304250263527211, 614889782588491411, 32589158477190044731, ...
%C 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 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 0 is a term because A006862(0) = 2 = 0^2 + 1^2 + 1^2.
%e 1 is a term because A006862(1) = 3 = 1^2 + 1^2 + 1^2.
%e 4 is a term because A006862(4) = 211 = 3^2 + 9^2 + 11^2.
%e 8 is a term because A006862(8) = 9699691 = 79^2 + 123^2 + 3111^2.
%o (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 a006862(n) = prod(k=1, n, prime(k))+1;
%o for(n=0, 200, if(!isA004215(a006862(n)), print1(n, ", ")));
%Y Cf. A004215, A006862.
%K nonn
%O 1,3
%A _Altug Alkan_, Jan 20 2016