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A267756
Indices of Euclid numbers (A006862) of the form x^2 + y^2 + z^2 where x, y and z are integers.
0
0, 1, 4, 8, 11, 12, 13, 15, 16, 19, 22, 27, 31, 34, 35, 38, 41, 42, 46, 48, 52, 53, 56, 57, 61, 62, 64, 65, 66, 69, 70, 71, 73, 74, 76, 77, 78, 79, 80, 83, 84, 86, 87, 88, 89, 91, 93, 95, 99, 100, 103, 104, 107, 108, 111, 112, 113, 115, 116, 118, 119, 124, 128, 131, 133
OFFSET
1,3
COMMENTS
Corresponding Euclid numbers are 2, 3, 211, 9699691, 200560490131, 7420738134811, 304250263527211, 614889782588491411, 32589158477190044731, ...
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, ...
Euclid numbers that are not of the form x^2 + y^2 + z^2 are 7, 31, 2311, 30031, 510511, 223092871, 6469693231, 13082761331670031, 1922760350154212639071, ...
EXAMPLE
0 is a term because A006862(0) = 2 = 0^2 + 1^2 + 1^2.
1 is a term because A006862(1) = 3 = 1^2 + 1^2 + 1^2.
4 is a term because A006862(4) = 211 = 3^2 + 9^2 + 11^2.
8 is a term because A006862(8) = 9699691 = 79^2 + 123^2 + 3111^2.
PROG
(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) ; }
a006862(n) = prod(k=1, n, prime(k))+1;
for(n=0, 200, if(!isA004215(a006862(n)), print1(n, ", ")));
CROSSREFS
Sequence in context: A311013 A311014 A311015 * A311016 A311017 A311018
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 20 2016
STATUS
approved