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A155925
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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.
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1
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1373, 1319, 1033, 1493, 853, 839, 593, 1093, 461, 487, 281, 821, 197, 263, 97, 677, 61, 167, 41, 661, 53, 199, 113, 773, 173, 359, 313, 1013, 421, 647, 641, 1381, 797, 1063, 1097, 1877, 1301, 1607, 2333, 1847, 1933, 2203, 2393, 3253, 2693, 3079, 3121, 4133
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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n a(n)
0 1373
1 1319
2 1033
3 1493
. . .
78 14561
79 0
80 15541
. . .
4686 87170273
4687 87198407
4688 0
4689 0
4690 0
4691 0
4692 0
4693 87413191
4694 0
4695 87516677
4696 87544133
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PROG
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(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); ) }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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