A263015 Integers n such that A007504(n) is the sum of 2 nonzero squares.

1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 15, 21, 25, 29, 35, 55, 58, 59, 64, 71, 85, 89, 93, 94, 95, 100, 101, 102, 108, 112, 114, 116, 122, 124, 130, 131, 133, 135, 141, 146, 147, 151, 159, 162, 165, 170, 171, 172, 177, 178, 183, 190, 192, 193, 194, 204, 205, 206

Offset

1,2

Comments

Integers n such that sum of the first n primes is the sum of 2 nonzero squares.

Initial values of corresponding sum of first n primes are 2, 5, 10, 17, 41, 58, 100, 160, 197 and 281.

Links

Table of n, a(n) for n=1..58.

Example

a(3) = 3 because 2 + 3 + 5 = 3^2 + 1^2.
a(5) = 6 because 2 + 3 + 5 + 7 + 11 + 13 = 5^2 + 4^2.
a(6) = 7 because 2 + 3 + 5 + 7 + 11 + 13 + 17 = 7^2 + 3^2.

Prog

(PARI) a(n) = sum(k=1, n, prime(k));
is(n) = { for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)) }
for(n=1, 1e3, if(is((a(n))), print1(n, ", ")))

Crossrefs

Cf. A000404, A007504.

Sequence in context: A257047 A192416 A026468 * A056176 A143831 A087072

Adjacent sequences: A263012 A263013 A263014 * A263016 A263017 A263018

Keyword

nonn

Author

Altug Alkan, Nov 27 2015

Status

approved