A140112 Primes of the form prime(x) + prime(x+1) + (prime(x+1)-prime(x))/2.

13, 37, 61, 71, 103, 131, 271, 277, 293, 311, 397, 457, 523, 541, 607, 743, 857, 1091, 1109, 1123, 1151, 1201, 1223, 1237, 1277, 1303, 1321, 1433, 1511, 1567, 1621, 1637, 1657, 1699, 1747, 1951, 2203, 2243, 2357, 2371, 2383, 2557, 2591, 2731, 2789, 2857

Offset

1,1

Links

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

Example

5+7+(7-5)/2=5+7+1=13

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[ 500]], 2, 1], PrimeQ] (* Harvey P. Dale, Mar 16 2022 *)

Crossrefs

Sequence in context: A319969 A045809 A238675 * A089030 A351537 A351536

Adjacent sequences: A140109 A140110 A140111 * A140113 A140114 A140115

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jun 21 2008

Extensions

More terms from Harvey P. Dale, Mar 16 2022

Status

approved