A131499 Primes p such that nextprime(p)=p+4 and previousprime(p)<p-4.

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

Offset

1,1

Comments

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,...

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

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.

Mathematica

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}]
Select[Prime[Range[400]], NextPrime[#]-#==4&&#-NextPrime[#, -1]>4&] (* Harvey P. Dale, Jul 16 2012 *)

Crossrefs

Sequence in context: A145486 A319673 A121764 * A217659 A054805 A141163

Adjacent sequences: A131496 A131497 A131498 * A131500 A131501 A131502

Keyword

nonn

Author

Zak Seidov, Aug 12 2007

Status

approved