A145871 Smallest k such that k^2+1 is divisible by A002144(n)^7.

32318, 6826318, 96940388, 7986582530, 24900904028, 92615568742, 416081467190, 988322434636, 3219884218827, 4867146503697, 26457926739667, 47023298541694, 26661771973542, 90980209992989, 257680081342861, 283410689912607

Offset

1,1

Links

Table of n, a(n) for n=1..16.

Example

a(2) = 6826318 since A002144(2) = 13, 6826318^2+1 = 46598617437125 = 5^3*13^7*13*457 and for no k < 6826318 does 13^7 divide k^2+1. a(4) = 7986582530 since A002144(4) = 29, 7986582530^2+1 = 63785500508501200901 = 29^7*197*409*45893 and for no k < 7986582530 does 29^7 divide k^2+1.

Prog

(PARI) {e=7; forprime(p=2, 40, if(p%4==1, q=p^e; m=q; while(!issquare(m-1, &n), m=m+q); print1(n, ", ")))}

Crossrefs

Cf. A002144 (primes of form 4n+1), A002313 (-1 is a square mod p), A059321, A145296, A145297, A145298, A145299, A145872, A145873.

Sequence in context: A137837 A115501 A218574 * A137283 A251875 A156038

Adjacent sequences: A145868 A145869 A145870 * A145872 A145873 A145874

Keyword

nonn

Author

Klaus Brockhaus, Oct 22 2008

Extensions

More terms from Klaus Brockhaus, Nov 12 2008

Status

approved