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Search: id:A155814
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| A155814 |
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Numbers n with the property that all four polynomials mentioned in A139414 evaluate at n to compositie numbers. |
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+0
2
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,10000
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PROGRAM
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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 { 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); ) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jan 28 2009]
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CROSSREFS
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Cf. A139414.
Sequence in context: A139503 A134240 A052162 this_sequence A135985 A142520 A140743
Adjacent sequences: A155811 A155812 A155813 this_sequence A155815 A155816 A155817
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Jan 28 2009
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 29 2009
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