A145871 -id:A145871 - cp's OEIS frontend

A145872 Smallest k such that k^2+1 is divisible by A002144(n)^8.

110443, 6826318, 3379649772, 61012922706, 1019349744435, 287369842623, 11331029931180, 71294762793847, 239822883201307, 923990886302412, 2369608176604944, 3156215819652023, 521749964271465, 2026364722410364

Offset: 1

Klaus Brockhaus, Oct 22 2008

nonn

			a(1) = 110443 since A002144(1) = 5, 110443^2+1 = 12197656250 = 2*5^8*13*1201 and for no k < 110443 does 5^8 divide k^2+1. a(3) = 3379649772 since A002144(3) = 17, 3379649772^2+1 = 11422032581379651985 = 5*13*17^8*97*259697 and for no k < 3379649772 does 17^8 divide k^2+1.

Cf. A002144 (primes of form 4n+1), A002313 (-1 is a square mod p), A059321, A145296, A145297, A145298, A145299, A145871, A145873.

{e=8; forprime(p=2, 40, if(p%4==1, q=p^e; m=q; while(!issquare(m-1, &n), m=m+q); print1(n, ",")))}

More terms from Klaus Brockhaus, Nov 12 2008

A145873 Smallest k such that k^2+1 is divisible by A002144(n)^9.

Original entry on oeis.org

280182, 822557039, 24306922095, 4563230639355, 15069267560119, 112076323050317, 50928660480181, 3138611770750343, 9110883894036198, 50251663587824641, 76004727767164666, 310872228812491206, 521749964271465

Offset: 1

Klaus Brockhaus, Oct 30 2008

nonn

			a(1) = 280182 since A002144(1) = 5, 280182^2+1 = 78501953125 = 5^9*40193 and for no k < 280182 does 5^9 divide k^2+1. a(3) = 24306922095 since A002144(3) = 17, 24306922095^2+1 = 590826461732399189026 = 2*17^9*29*673*127637 and for no k < 24306922095 does 17^9 divide k^2+1.

Cf. A002144 (primes of form 4n+1), A002313 (-1 is a square mod p), A059321, A145296, A145297, A145298, A145299, A145871, A145872.

cp's OEIS Frontend

A145872 Smallest k such that k^2+1 is divisible by A002144(n)^8.

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