A095672 Primes p = p_(n+1) such that p_n + p_(n+2) = 2*p_(n+1) + 4.

31, 61, 73, 151, 271, 293, 337, 401, 433, 491, 547, 571, 577, 601, 743, 761, 839, 911, 1033, 1039, 1063, 1201, 1231, 1291, 1321, 1409, 1453, 1531, 1571, 1621, 1627, 2003, 2017, 2039, 2131, 2243, 2273, 2341, 2383, 2551, 2663, 2713, 2719, 2791, 3041, 3049

Offset

1,1

Comments

Primes that are first prime chords.

These come from music based on the prime differences where the chords are an even number of note steps from the primary note.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

31 is a term because 29+37 = 2*31 + 4 = 66.

Maple

primes:= select(isprime, [seq(i, i=3..10000, 2)]):
L:= primes[1..-3]+primes[3..-1]-2*primes[2..-2]:
primes[select(t -> L[t-1]=4, [$2..nops(L)+1])]; # Robert Israel, Jun 28 2018

Mathematica

m = 1; Prime[1 + Select[ Range[450], Prime[ # + 2] - 2*Prime[ # + 1] + Prime[ # ] - 4*m == 0 &]] (* Robert G. Wilson v, Jul 14 2004 *)
Select[Partition[Prime[Range[500]], 3, 1], #[[1]]+#[[3]]==2#[[2]]+4&][[;; , 2]] (* Harvey P. Dale, Jan 31 2024 *)

Crossrefs

Cf. A095419, A095420, A095648, A095649, A095650, A095651, A095673.

Sequence in context: A189556 A185934 A052158 * A073650 A078562 A054804

Adjacent sequences: A095669 A095670 A095671 * A095673 A095674 A095675

Keyword

nonn

Author

Roger L. Bagula, Jul 02 2004

Extensions

Edited by Robert G. Wilson v, Jul 14 2004

Description corrected by N. J. A. Sloane, Jul 19 2004

Status

approved