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%I #34 Jan 25 2022 13:01:08
%S 93,117,118,119,120,121,122,123,143,144,145,185,186,187,203,204,205,
%T 206,207,215,216,217,218,219,245,246,247,287,288,289,297,298,299,300,
%U 301,302,303,321,322,323,324,325,326,327,341,342,343,363,393,405,413,414
%N Composite numbers having six composite nearest-neighbors.
%C Terms lie between primes separated by a gap of at least 8 (see A083371). - _David A. Corneth_, Jun 24 2016
%H G. C. Greubel, <a href="/A167776/b167776.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1)=117 (114,115,116,118,119,120 are composite nearest-neighbors);
%e a(2)=118 (115,116,117,119,120,121 are composite nearest-neighbors).
%e 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
%t Select[Range[6!],!PrimeQ[#] && !PrimeQ[#-1] && !PrimeQ[#+1] && !PrimeQ[#-2] && !PrimeQ[#+2] && !PrimeQ[#-3] && !PrimeQ[#+3]&] (* _Vladimir Joseph Stephan Orlovsky_, Dec 26 2010 *)
%t Select[Range@ 414, Times @@ Boole@ Map[CompositeQ, Range[# - 3, # + 3]] == 1 &] (* _Michael De Vlieger_, Jun 24 2016 *)
%o (PARI) lista(n) = {forprime(i=2,n+3,g=nextprime(i+1)-i;
%o for(j=i+4,i+g-4,print1(j", ")))}
%o a(n) = {forprime(i=88,,g=nextprime(i+1)-i;n-=max(0,g-7);
%o if(n<=0,return(i+g-4+n)))}
%o \\ gives the next term larger than n, whether n is a term or not.
%o 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
%Y Cf. A002808, A079364, A083371, A167705.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Nov 11 2009
%E Corrected (93, 144, 145 inserted) by _R. J. Mathar_, May 30 2010
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