A140111 Primes of the form prime(x) + prime(x+1) - (prime(x+1) - prime(x))/2.

7, 11, 23, 59, 83, 97, 109, 149, 233, 283, 317, 337, 349, 359, 367, 383, 479, 487, 563, 571, 593, 641, 709, 769, 823, 839, 863, 1009, 1117, 1129, 1217, 1283, 1297, 1319, 1423, 1553, 1579, 1619, 1627, 1663, 1733, 1913, 2029, 2039, 2063, 2069, 2083, 2099, 2129

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 21 2008

Keywords

• nonn

Examples

			3+5-(5-3)/2=3+5-1=7, 5+7-(7-5)/2=5+7-1=11, ...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A092217.

Programs

Mathematica

a = {}; Do[p1 = Prime[n]; p2 = Prime[n + 1]; p = p1 + p2 - (p2 - p1)/2; If[PrimeQ[p], AppendTo[a, p]], {n, 10^2}]; a
Select[#[[1]]+#[[2]]-(#[[2]]-#[[1]])/2&/@Partition[ Prime[ Range[ 200]],2,1],PrimeQ] (* Harvey P. Dale, Mar 14 2021 *)

Extensions

More terms from Harvey P. Dale, Mar 14 2021