A221309 -id:A221309 - cp's OEIS frontend

A079364 Composite numbers having two composite neighbors.

9, 15, 21, 25, 26, 27, 33, 34, 35, 39, 45, 49, 50, 51, 55, 56, 57, 63, 64, 65, 69, 75, 76, 77, 81, 85, 86, 87, 91, 92, 93, 94, 95, 99, 105, 111, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 129, 133, 134, 135, 141, 142, 143, 144, 145, 146, 147, 153, 154, 155

Offset: 1

Reinhard Zumkeller, Feb 15 2003

nonn

In other words, composite numbers that are not nearest-neighbors of primes. - Omar E. Pol, Jan 02 2009

Complement of A210940. - Omar E. Pol, Apr 18 2012

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000040, A002808, A014574, A045718.

Cf. A010051, A221309 (subsequence).

a079364 n = a079364_list !! (n-1)
a079364_list = filter
   (\x -> a010051' (x - 1) == 0 && a010051' (x + 1) == 0) a002808_list
-- Reinhard Zumkeller, Jan 10 2013

Select[Range[6! ],!PrimeQ[ # ]&&!PrimeQ[ #-1]&&!PrimeQ[ #+1]&] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2010 *)
With[{r=Complement[Range[160],Prime[Range[PrimePi[160]]]]}, Transpose[ Select[ Partition[r,3,1], Differences[#]=={1,1}&]][[2]]] (* Harvey P. Dale, Feb 05 2012 *)
Mean/@SequencePosition[Table[If[CompositeQ[n],1,0],{n,200}],{1,1,1}] (* Harvey P. Dale, May 10 2025 *)

A117499 Number of subsets of {n-1, n, n+1} that sum up to a prime.

Original entry on oeis.org

4, 4, 4, 3, 2, 4, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 0, 1, 1, 1, 2, 4, 2, 1, 1, 1, 1, 3, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 0, 2, 2, 1, 1, 2, 2, 2, 0, 1, 1, 1, 2, 3, 1, 0, 0, 0, 1, 3, 2, 2, 2, 2, 1, 2, 1, 1, 1

Offset: 1

Reinhard Zumkeller, Mar 23 2006

nonn

0 <= a(n) <= 4; a(A066388(n)) = 4.

a(A221309(n)) = 0; a(A221310(n)) = 4. - Reinhard Zumkeller, Jan 10 2013

			a(1) = #{2, 0+2=2, 1+2=3, 0+1+2=3} = 4;
a(2) = #{2, 3, 1+2=3, 2+3=5} = 4;
a(3) = #{2, 3, 2+3=5, 3+4=7} = 4;
a(4) = #{3, 5, 3+4=7} = 3;
a(5) = #{5, 5+6=11} = 2.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A010051.

a117499 1 = sum $ map a010051 [1, 2, 0 + 1, 0 + 2, 1 + 2, 0 + 1 + 2]
a117499 n = sum $ map a010051 [n - 1, n, n + 1, 2 * n - 1, 2 * n + 1]
-- Reinhard Zumkeller, Jan 10 2013

Table[Length[Select[{-1+n,n,1+n,-1+2 n,2 n,1+2 n,3 n},PrimeQ]],{n,105}]
ssp[{a_,b_,c_}]:=Count[Subsets[{a,b,c},3],?(PrimeQ[Total[#]]&)]; ssp/@ Partition[ Range[0,110],3,1] (* _Harvey P. Dale, Jan 29 2013 *)

a(n) = A010051(n-1) + A010051(n) + A010051(n+1) + A010051(2*n-1) + A010051(2*n) + A010051(2*n+1).

cp's OEIS Frontend

A079364 Composite numbers having two composite neighbors.

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