A155925 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.

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

Offset

0,1

Comments

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.

Links

Harry J. Smith, Table of n, a(n) for n = 0..10000

Example

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

Prog

(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); ) }

Crossrefs

Cf. A139414.

Sequence in context: A371191 A181969 A139414 * A329917 A060981 A140125

Adjacent sequences: A155922 A155923 A155924 * A155926 A155927 A155928

Keyword

nonn

Author

Harry J. Smith, Jan 31 2009

Status

approved