

A155814


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


2



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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: 46884692. An example of exactly 7 consecutive terms in the sequence: 1475314759.


LINKS

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


PROG

(PARI) p1(n)=4*n*n146*n+1373 p2(n)=4*n*n144*n+1459 p3(n)=4*n*n142*n+1301 p4(n)=4*n*n140*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



