A169546 -id:A169546 - cp's OEIS frontend

A100317 Numbers k such that exactly one of k - 1 and k + 1 is prime.

1, 2, 3, 8, 10, 14, 16, 20, 22, 24, 28, 32, 36, 38, 40, 44, 46, 48, 52, 54, 58, 62, 66, 68, 70, 74, 78, 80, 82, 84, 88, 90, 96, 98, 100, 104, 106, 110, 112, 114, 126, 128, 130, 132, 136, 140, 148, 152, 156, 158, 162, 164, 166, 168, 172, 174, 178, 182, 190, 194, 196, 200

Offset: 1

Rick L. Shepherd, Nov 13 2004

nonn

Beginning with a(2) = 3, n such that exactly one of n - 1 and n + 1 is composite.

			3 is in the sequence because 2 is prime but 4 is composite.
4 is not in the sequence because both 3 and 5 are prime.
5 is not in the sequence either because both 4 and 6 are composite.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A100318 (at least one of n - 1 and n + 1 is composite).

Cf. A001477, A169546, A171689, A099049, A014574 (no intersection with this sequence).

[n: n in [1..250] | IsPrime(n-1) xor IsPrime(n+1) ]; // G. C. Greubel, Apr 25 2019

Select[Range[250], Xor[PrimeQ[# - 1], PrimeQ[# + 1]] &] (* G. C. Greubel, Apr 25 2019 *)
Module[{nn=Table[If[PrimeQ[n],1,0],{n,0,220}],t1,t2},t1=Mean/@ SequencePosition[ nn,{1,,0}];t2=Mean/@SequencePosition[nn,{0,,1}];Flatten[ Join[t1,t2]]//Sort]-1 (* Harvey P. Dale, Jul 13 2019 *)

for(n=1,250,if(isprime(n-1)+isprime(n+1)==1,print1(n,",")))

[n for n in (1..250) if (is_prime(n-1) + is_prime(n+1) == 1)] # G. C. Greubel, Apr 25 2019

A171611 From Goldbach problem: number of decompositions of 2n into unordered sums of two primes > 3.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 3, 2, 2, 3, 1, 3, 4, 2, 2, 4, 2, 3, 5, 3, 3, 5, 2, 4, 6, 2, 4, 6, 2, 4, 6, 4, 4, 7, 4, 4, 8, 4, 4, 9, 3, 5, 7, 3, 5, 8, 4, 5, 8, 5, 6, 10, 5, 6, 12, 4, 5, 10, 3, 6, 9, 5, 5, 8, 6, 7, 11, 6, 5, 12, 3, 7, 11, 5, 7, 10, 5, 5, 13, 8, 6, 11, 6, 7, 14, 5, 7, 13, 5, 8, 11, 6, 8, 13

Offset: 1

Juri-Stepan Gerasimov, Dec 13 2009

nonn

			a(5)=1 because 2*5 = 5 + 5.

Lei Zhou, Table of n, a(n) for n = 1..10000

Cf. A045917, A169546.

A171611 := proc(n) a := 0 ; for i from 3 do p := ithprime(i) ; q := 2*n-p ; if q < p then return a ; end if; if isprime(q) then a := a+1 ; end if; if q <= p then return a ; end if; end do: end proc:
seq(A171611(n), n=1..120) ; # R. J. Mathar, May 22 2010

Table[s = 2*n; ct = 0; p = 3; While[p = NextPrime[p]; p <= n, If[PrimeQ[s - p], ct++]]; ct, {n, 100}] (* Lei Zhou, Apr 10 2014 *)

a(38) changed from 5 to 4 and a(79) and a(82) changed by R. J. Mathar, May 22 2010

A171387 The characteristic function of primes > 3: 1 if n is prime such that neither prime+-1 is prime else 0.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0

Offset: 1

Juri-Stepan Gerasimov, Dec 07 2009

nonn

Antti Karttunen, Table of n, a(n) for n = 1..1001
Index entries for characteristic functions

Cf. A000007, A010051, A063524, A080545, A169546, A171386.

A010051(n) = a(n) + A171386(n).

If n > 3, a(n) = A010051(n), otherwise a(n) = 0. - Antti Karttunen, Oct 04 2017

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A100317 Numbers k such that exactly one of k - 1 and k + 1 is prime.

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A171611 From Goldbach problem: number of decompositions of 2n into unordered sums of two primes > 3.

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A171387 The characteristic function of primes > 3: 1 if n is prime such that neither prime+-1 is prime else 0.

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