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%I #10 Sep 05 2018 02:30:13
%S 1373,1319,1033,1493,853,839,593,1093,461,487,281,821,197,263,97,677,
%T 61,167,41,661,53,199,113,773,173,359,313,1013,421,647,641,1381,797,
%U 1063,1097,1877,1301,1607,2333,1847,1933,2203,2393,3253,2693,3079,3121,4133
%N a(x) = if one of {4x^2 - 146x + 1373, 4x^2 - 144x + 1459, 4x^2 - 142x + 1301, 4x^2 - 140x + 1877} is prime, then pick that prime in sequence, otherwise pick zero.
%C The polynomials are tested in a cycle beginning with a(1 + x mod 4), i.e., when x == 0 (mod 4), they are tested in order t1,t2,t3,t4; when x == 1 (mod 4), they are tested in the order t2,t3,t4,t1. If none of the polynomials are prime, a zero value is given.
%H Harry J. Smith, <a href="/A155925/b155925.txt">Table of n, a(n) for n = 0..10000</a>
%e n a(n)
%e 0 1373
%e 1 1319
%e 2 1033
%e 3 1493
%e . . .
%e 78 14561
%e 79 0
%e 80 15541
%e . . .
%e 4686 87170273
%e 4687 87198407
%e 4688 0
%e 4689 0
%e 4690 0
%e 4691 0
%e 4692 0
%e 4693 87413191
%e 4694 0
%e 4695 87516677
%e 4696 87544133
%o (PARI) p1(n)=4*n*n-146*n+1373 p2(n)=4*n*n-144*n+1459 p3(n)=4*n*n-142*n+1301 p4(n)=4*n*n-140*n+1877 { for (n=0, 10000, t1=p1(n); t2=p2(n); t3=p3(n); t4=p4(n); if (n%4==0, b1=t1; b2=t2; b3=t3; b4=t4; ); if (n%4==1, b1=t2; b2=t3; b3=t4; b4=t1; ); if (n%4==2, b1=t3; b2=t4; b3=t1; b4=t2; ); if (n%4==3, b1=t4; b2=t1; b3=t2; b4=t3; ); a=0; if (isprime(b1), a=b1); if (a==0 && isprime(b2), a=b2); if (a==0 && isprime(b3), a=b3); if (a==0 && isprime(b4), a=b4); print(n," ",a); write("b155925.txt",n," ",a); ) }
%Y Cf. A139414.
%K nonn
%O 0,1
%A _Harry J. Smith_, Jan 31 2009
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