A167776 Composite numbers having six composite nearest-neighbors.

93, 117, 118, 119, 120, 121, 122, 123, 143, 144, 145, 185, 186, 187, 203, 204, 205, 206, 207, 215, 216, 217, 218, 219, 245, 246, 247, 287, 288, 289, 297, 298, 299, 300, 301, 302, 303, 321, 322, 323, 324, 325, 326, 327, 341, 342, 343, 363, 393, 405, 413, 414

Offset

1,1

Comments

Terms lie between primes separated by a gap of at least 8 (see A083371). - David A. Corneth, Jun 24 2016

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Example

a(1)=117 (114,115,116,118,119,120 are composite nearest-neighbors);
a(2)=118 (115,116,117,119,120,121 are composite nearest-neighbors).
There are no primes between primes 241 and 251 which gives a gap of 10 between them. Therefore, all numbers between (inclusive) 241 + 4 and 251 - 4 are terms. - David A. Corneth, Jun 24 2016

Mathematica

Select[Range[6!], !PrimeQ[#] && !PrimeQ[#-1] && !PrimeQ[#+1] && !PrimeQ[#-2] && !PrimeQ[#+2] && !PrimeQ[#-3] && !PrimeQ[#+3]&] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)
Select[Range@ 414, Times @@ Boole@ Map[CompositeQ, Range[# - 3, # + 3]] == 1 &] (* Michael De Vlieger, Jun 24 2016 *)

Prog

(PARI) lista(n) = {forprime(i=2, n+3, g=nextprime(i+1)-i;
for(j=i+4, i+g-4, print1(j", ")))}
a(n) = {forprime(i=88, , g=nextprime(i+1)-i; n-=max(0, g-7);
if(n<=0, return(i+g-4+n)))}
\\ gives the next term larger than n, whether n is a term or not.
nxt(n) = my(p=nextprime(n), g=0); if(p-n>4, n+1, while(1, q=nextprime(p+1); g=q-p; if(g>7, return(p+4), p=q))) \\ David A. Corneth, Jun 24 2016

Crossrefs

Cf. A002808, A079364, A083371, A167705.

Sequence in context: A118131 A020320 A039550 * A099019 A082131 A249300

Adjacent sequences: A167773 A167774 A167775 * A167777 A167778 A167779

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 11 2009

Extensions

Corrected (93, 144, 145 inserted) by R. J. Mathar, May 30 2010

Status

approved