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Search: id:A131499
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| A131499 |
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Primes p such that nextprime(p)=p+4 and previousprime(p)<p-4. |
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| 37, 67, 79, 97, 127, 163, 223, 277, 307, 379, 397, 439, 457, 487, 499, 613, 673, 739, 757, 769, 853, 877, 907, 937, 967, 1009, 1087, 1213, 1297, 1423, 1447, 1549, 1567, 1579, 1597, 1663, 1693, 1783, 1867, 1993, 2137, 2203, 2293, 2347, 2377, 2389, 2437
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Or a=p+1, b=p+2, and c=p+3 are composite triples: a,b,c are composite while a-1 and c+1 are not. There are no composite twins, and composite singles are interprimes of twin primes. All numbers are congruent to 1 mod 6 (and not congruent to 1 mod 10). First differences divided by 6 are: 5,2,3,5,6,10,9,5,12,3,7,3,5,2,19,10,11,3,2,14,4,5,5,5,7,13,21,14,21,4,17,...
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EXAMPLE
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a(1)=37 because nextprime(37)=41=37+4 and previousprime(37)=31<37-4,
a(2)=67 because nextprime(67)=71=67+4 and previousprime(67)=61<67-4.
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MATHEMATICA
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p1000=Prime[Range[1000]]; c=0; Do[p=p1000[[i]]; If[p-p1000[[i-1]]>4&&p1000[[i+1]]==4+p, c++; a[c]=p], {i, 2, 999}]; Table[a[i], {i, c}]
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CROSSREFS
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Sequence in context: A117475 A145486 A121764 this_sequence A054805 A139602 A141163
Adjacent sequences: A131496 A131497 A131498 this_sequence A131500 A131501 A131502
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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), Aug 12 2007
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