A191472 a(n) = 2*prime(n+2) - prime(n+1) - prime(n).

5, 6, 10, 8, 10, 8, 10, 16, 10, 14, 14, 8, 10, 16, 18, 10, 14, 14, 8, 14, 14, 16, 22, 16, 8, 10, 8, 10, 32, 22, 16, 10, 22, 14, 14, 18, 14, 16, 18, 10, 22, 14, 10, 8, 26, 36, 20, 8, 10, 16, 10, 22, 22, 18, 18, 10, 14, 14, 8, 22, 38, 22, 8, 10, 32, 26, 26, 14

Offset: 1

Author

Zak Seidov, Aug 27 2012

Keywords

• nonn

Comments

For n > 2, all terms >= 8 and all even integers are possible except for 12.

Examples

			a(1) = 2*prime(3) - prime(2) - prime(1) = 2*5 - 3 - 2 = 5.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000
• Charles R Greathouse IV, Record values

Crossrefs

Cf. A096379.

Programs

Mathematica

ps = Prime[Range[100]]; Table[2*ps[[n+2]] - ps[[n+1]] - ps[[n]], {n, Length[ps] - 2}] (* T. D. Noe, Aug 27 2012 *)
2#[[3]]-#[[2]]-#[[1]]&/@Partition[Prime[Range[70]],3,1] (* Harvey P. Dale, Aug 10 2023 *)
ListConvolve[{2, -1, -1}, Prime[Range[100]]] (* Paolo Xausa, Jul 30 2024 *)

PARI

first(n)=my(v=vector(n),p=2,q=3,k); forprime(r=5,, if(k++>n, break); v[k]=2*r-q-p; p=q; q=r); v \\ Charles R Greathouse IV, Oct 03 2017