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%I #26 Jun 06 2014 18:20:01
%S 73,89,113,233,257,281,337,353,577,593,601,617,881,937,1033,1049,1097,
%T 1153,1193,1201,1217,1249,1289,1433,1481,1553,1601,1609,1721,1753,
%U 1777,1801,1889,1913,2089,2113,2129,2273,2281,2393,2441,2473,2593,2657,2689
%N Primes p == 1 mod 8 such that 2 and -2 are both 4th powers (one implies other) mod p.
%C Primes p such that x^4 == 2 has more than two (in fact four) solutions mod p. This is the sequence of terms common to A040098 (primes p such that x^4 == 2 has a solution mod p) and A007519 (primes of form 8n+1). Solutions mod p are represented by integers from 0 to p - 1. For p > 2, i is a solution mod p of x^4 == 2 iff p - i is a solution mod p of x^4 == 2, thus the sum of first and fourth solution is p and so is the sum of second and third solution. The solutions are given in A065909, A065910, A065911 and A065912. - _Klaus Brockhaus_, Nov 28 2001
%C Primes of the form x^2+64y^2. - _T. D. Noe_, May 13 2005
%H N. J. A. Sloane and Vincenzo Librandi, <a href="/A014754/b014754.txt">Table of n, a(n) for n = 1..9769</a> (the first 1000 terms were found by Vincenzo Librandi)
%o (PARI) A014754(m) = local(p,s,x,z); forprime(p = 3,m,s = []; for(x = 0,p-1, if(x^4%p == 2%p,s = concat(s,[x]))); z = matsize(s)[2]; if(z>2,print1(p,",")))
%o (PARI) {a(n) = local(m, c, x); if( n<1, 0, c = 0; m = 1; while( c<n, m++; if( isprime(m), x = 0; for(y=1, sqrtint( m \ 64 ), if( issquare( m - 64 * y^2, &x), break)); if( x, c++ ))); m)} /* _Michael Somos_, Mar 22 2008 */
%o (PARI) forprime(p=1, 9999, p%8==1&&ispower(Mod(2, p), 4)&&print1(p", ")) \\ _M. F. Hasler_, Feb 18 2014
%o (PARI) is_A014754(p)={p%8==1&&ispower(Mod(2, p), 4)&&isprime(p)} \\ _M. F. Hasler_, Feb 18 2014
%Y Cf. A040098, A007519, A014754, A007522, A065909, A065910, A065911, A065912, A070179.
%K nonn
%O 1,1
%A _Warren D. Smith_
%E Removed erroneous Mma program; extended b-file using first PARI program of _M. F. Hasler_. - _N. J. A. Sloane_, Jun 06 2014
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