A145299 Smallest k such that k^2+1 is divisible by A002144(n)^6.

1068, 1999509, 390112, 253879357, 756360062, 2363588163, 5041394261, 9435321777, 41865466758, 102666405913, 197177418061, 316411915250, 171829799914, 625667121807, 182312430890, 1095001339019, 6390289199260

Offset

1,1

Links

Table of n, a(n) for n=1..17.

Example

a(1) = 1068 since A002144(1) = 5, 1068^2+1 = 1140625 = 5^6*73 and for no k < 1068 does 5^6 divide k^2+1. a(11) = 197177418061 since A002144(11) = 97, 197177418061^2+1 = 38878934193202368999722 = 2*97^6*23337479509 and for no k < 197177418061 does 97^6 divide k^2+1.

Prog

(PARI) { e=6; forprime(p=2, 1000, if(p%4==1, k=lift(sqrt(-1+O(p^e))); if(k>p^e/2, k=p^e-k); print1(k, ", "))) }

Crossrefs

Cf. A002144 (primes of form 4n+1), A002313 (-1 is a square mod p), A059321, A145296, A145297, A145298.

Sequence in context: A234880 A218565 A145298 * A328894 A289702 A095673

Adjacent sequences: A145296 A145297 A145298 * A145300 A145301 A145302

Keyword

nonn

Author

Klaus Brockhaus, Oct 17 2008

Extensions

More terms and efficient PARI program from. - Max Alekseyev, Oct 28 2008

Status

approved