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

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, ...

Links

Table of n, a(n) for n=1..65.

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

Cf. A004215, A006862.

Sequence in context: A311013 A311014 A311015 * A311016 A311017 A311018

Adjacent sequences: A267753 A267754 A267755 * A267757 A267758 A267759

Keyword

nonn

Author

Altug Alkan, Jan 20 2016

Status

approved