A134099 Odd nonprimes np such that np-2 is a prime number but np+2 is not.

25, 33, 49, 55, 63, 75, 85, 91, 115, 133, 141, 153, 159, 169, 175, 183, 201, 213, 235, 243, 253, 259, 265, 273, 285, 295, 319, 333, 339, 355, 361, 369, 375, 385, 391, 403, 411, 423, 435, 445, 451, 469, 481, 493, 505, 511, 525, 543, 549, 559, 565, 573, 579

Offset

1,1

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

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

Mathematica

Select[Range[5, 1000, 2], !PrimeQ[#] && PrimeQ[#-2] && !PrimeQ[#+2]&] (* Vladimir Joseph Stephan Orlovsky, Feb 03 2012 *)
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 *)
Select[Partition[Range[600], 5, 2], PrimeQ[#[[1]]]&&AllTrue[{#[[3]], #[[5]]}, CompositeQ]&][[;; , 3]] (* Harvey P. Dale, May 14 2023 *)

Prog

(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

Crossrefs

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

Sequence in context: A131610 A211466 A269345 * A129074 A188443 A068411

Adjacent sequences: A134096 A134097 A134098 * A134100 A134101 A134102

Keyword

easy,nonn

Author

Enoch Haga, Oct 08 2007

Extensions

Definition corrected by Jens Voß, Mar 12 2014

Definition modified by Harvey P. Dale, May 14 2023

Status

approved