A263674 Double interprimes: a(n) = (q+r)/2 = (p+s)/2 with p<q<r<s consecutive primes.

9, 12, 15, 18, 30, 42, 60, 81, 102, 105, 108, 120, 144, 165, 186, 195, 228, 260, 270, 312, 363, 381, 399, 420, 426, 441, 462, 489, 495, 552, 570, 582, 600, 696, 705, 714, 765, 816, 825, 858, 870, 882, 897, 924, 987, 1026, 1050, 1056, 1092, 1113, 1167, 1230

Offset

1,1

Comments

Values of p (lesser of consecutive primes) are in the sequence A022885.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Interprime

Example

600 is in this sequence because 593, 599, 601 and 607 are consecutive primes, and 600 = (599+601)/2 = (593+607)/2.

Mathematica

(Prime@ # + Prime[# + 3])/2 & /@ Select[Range@ 240, (First@ # + Last@ #)/2 == (#[[2]] + #[[3]])/2 &@ Prime@ Range[#, # + 3] & (* Michael De Vlieger, Nov 18 2015 *)
Mean/@Select[Partition[Prime[Range[300]], 4, 1], (#[[2]]+#[[3]])/2==(#[[1]]+#[[4]])/2&] (* Harvey P. Dale, Aug 18 2024 *)

Prog

(PARI) {forprime(q=3, 2000, p=precprime(q-1); r=nextprime(q+1); s=nextprime(r+1); m=(q+r)/2; if(m==(p+s)/2, print1(m, ", ")))}

Crossrefs

Cf. A022885, A075190, A075277, A075296, A078443, A130178, A263675, A263676.

Sequence in context: A102655 A308748 A120167 * A337701 A048699 A019468

Adjacent sequences: A263671 A263672 A263673 * A263675 A263676 A263677

Keyword

nonn

Author

Antonio Roldán, Oct 23 2015

Status

approved