A155814 Numbers n with the property that all four polynomials mentioned in A139414 evaluate at n to composite numbers.

79, 127, 203, 234, 243, 255, 324, 325, 326, 350, 361, 402, 406, 416, 430, 445, 447, 471, 490, 509, 513, 527, 531, 539, 548, 553, 561, 564, 572, 602, 604, 627, 630, 631, 633, 640, 653, 654, 656, 694, 695, 703, 704, 715, 720, 735, 783, 790, 791, 812, 813, 818

Offset

1,1

Comments

The four polynomials considered in A139414 are 1373 - 146*n + 4*n^2, 1459 - 144*n + 4*n^2, 1301 - 142*n + 4*n^2, 1877 - 140*n + 4*n^2. For n=79 these are all composite: 14803, 15047, 15047, 15781.

An example of exactly 5 consecutive terms in the sequence: 4688-4692. An example of exactly 7 consecutive terms in the sequence: 14753-14759.

Links

Harry J. Smith, Table of n, a(n) for n = 1..10000

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 { n=0; for (p=0, 45837, a1=p1(p); a2=p2(p); a3=p3(p); a4=p4(p); if (!isprime(a1) && !isprime(a2) && !isprime(a3) && !isprime(a4), n++; a=p; print(n, " ", a); write("b155814.txt", n, " ", a); ) ) } \\ Harry J. Smith, Jan 28 2009

Crossrefs

Cf. A139414.

Sequence in context: A139503 A134240 A052162 * A135985 A142520 A140743

Adjacent sequences: A155811 A155812 A155813 * A155815 A155816 A155817

Keyword

nonn

Author

Zak Seidov, Jan 28 2009

Extensions

Edited by N. J. A. Sloane, Jan 29 2009

Status

approved