A078765 Prime numbers occurring at integer Pythagorean distance (radius) from 1 in Ulam square prime-spiral. Primes on axes are excluded.

227, 239, 271, 997, 1021, 1061, 2243, 2251, 2311, 2339, 2347, 3527, 4153, 4217, 6311, 6491, 6551, 6971, 9059, 9109, 9133, 9341, 9397, 12671, 14549, 16273, 16369, 16529, 19507, 20551, 20611, 20719, 20899, 20983, 25301, 25343, 25621, 25741, 27893

Offset

1,1

Comments

Note that prime numbers on an axis are automatically an integer distance from 1.

Links

Table of n, a(n) for n=1..39.

Example

a(1) = 227, a prime number: distance from 1 off-axis = (6,8,10) triangle.

Prog

(PARI) { uc(n) = k = (sqrtint(4*n-3)-1)\2; d=n-1-k*(k+1); if(k%2, c=[(k+1)\2-min(d, k+1), (k+1)\2-max(d-k-1, 0)], c=[-k\2+min(d, k+1), -k\2+max(d-k-1, 0)] ); c }
forprime(p=2, 10^5, t=uc(p); if( t[1]!=0 && t[2]!=0 && issquare(t[1]^2+t[2]^2), print1(p, ", "))) \\ Max Alekseyev

Crossrefs

Sequence in context: A098247 A092994 A031513 * A179141 A259059 A333425

Adjacent sequences: A078762 A078763 A078764 * A078766 A078767 A078768

Keyword

nonn

Author

Donald S. McDonald, Jan 09 2003

Extensions

More terms from Max Alekseyev, Jan 28 2012

Status

approved