A145872 -id:A145872 - cp's OEIS frontend

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

Klaus Brockhaus, Oct 22 2008

nonn

			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.

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

{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, ",")))}

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

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

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