A134099 - OEIS

%I #29 May 14 2023 16:55:27

%S 25,33,49,55,63,75,85,91,115,133,141,153,159,169,175,183,201,213,235,

%T 243,253,259,265,273,285,295,319,333,339,355,361,369,375,385,391,403,

%U 411,423,435,445,451,469,481,493,505,511,525,543,549,559,565,573,579

%N Odd nonprimes np such that np-2 is a prime number but np+2 is not.

%C Primes referred to in the example are found in A124582 (see A083370 and compare A124582).

%H Vincenzo Librandi, <a href="/A134099/b134099.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 25 because it is an odd nonprime preceded by the prime 23 and followed by the odd nonprime 27.

%t Select[Range[5,1000,2], !PrimeQ[#] && PrimeQ[#-2] && !PrimeQ[#+2]&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 03 2012 *)

%t 2#-1&/@(Mean/@SequencePosition[Table[If[PrimeQ[n],1,0],{n,1,601,2}],{1,0,0}]) (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 31 2020 *)

%t Select[Partition[Range[600],5,2],PrimeQ[#[[1]]]&&AllTrue[{#[[3]],#[[5]]},CompositeQ]&][[;;,3]] (* _Harvey P. Dale_, May 14 2023 *)

%o (UBASIC) 10 'primes using counters 20 N=3:print "2 ";:print "3 ";:C=2 30 A=3:S=sqrt(N) 40 B=N\A 50 if B*A=N then 55 55 Q=N+2:R=N-2: if Q<>prmdiv(Q) and N<>prmdiv(N) and R=prmdiv(R) then print Q;N;R;"-";:stop:else N=N+2:goto 30 60 A=A+2 70 if A<=sqrt(N) then 40:stop 81 C=C+1 100 N=N+2:goto 30

%Y Cf. A124582, A083370, A134100, A134101, A007510.

%K easy,nonn

%O 1,1

%A _Enoch Haga_, Oct 08 2007

%E Definition corrected by _Jens Voß_, Mar 12 2014

%E Definition modified by _Harvey P. Dale_, May 14 2023