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A267756
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Indices of Euclid numbers (A006862) of the form x^2 + y^2 + z^2 where x, y and z are integers.
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0
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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
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OFFSET
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1,3
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COMMENTS
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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, ...
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LINKS
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Table of n, a(n) for n=1..65.
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EXAMPLE
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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.
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PROG
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(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, ", ")));
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CROSSREFS
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Cf. A004215, A006862.
Sequence in context: A311013 A311014 A311015 * A311016 A311017 A311018
Adjacent sequences: A267753 A267754 A267755 * A267757 A267758 A267759
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KEYWORD
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nonn
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AUTHOR
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Altug Alkan, Jan 20 2016
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STATUS
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approved
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