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Numbers k such that neither k-1 nor k+1 is prime or semiprime.
1

%I #10 Feb 04 2019 02:12:39

%S 0,17,19,29,31,41,43,49,51,53,55,65,67,69,71,77,79,89,91,97,99,101,

%T 103,109,111,113,115,125,127,129,131,137,139,149,151,153,155,161,163,

%U 169,171,173,175,181,183,185,187,189,191,197,199,209,211,221,223,229,231

%N Numbers k such that neither k-1 nor k+1 is prime or semiprime.

%C a(n+1) is the (n+2)-th odd sum of two consecutive nonnegative nonprimes.

%H Harvey P. Dale, <a href="/A176462/b176462.txt">Table of n, a(n) for n = 1..2000</a>

%F a(n+1) = A166685(n+2).

%e 0 is a term because neither 0-1=-1 nor 0+1=1 is prime or semiprime.

%p isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc: for n from 0 to 400 do if isA001358(n+1) or isA001358(n-1) or isprime(n+1) or isprime(n-1) then ; else printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Apr 20 2010

%t Join[{0},Flatten[Position[Partition[Table[If[PrimeQ[n]||PrimeOmega[n] == 2,1,0],{n,250}],3,1],_?(#[[1]]==#[[3]]==0&),{1},Heads -> False]]+ 1] (* _Harvey P. Dale_, Oct 27 2015 *)

%Y Cf. A141468.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Apr 18 2010

%E Entries checked by _R. J. Mathar_, Apr 20 2010