A293395 The initial member of 5 consecutive primes whose arithmetic mean is the middle member.

71, 271, 337, 431, 631, 661, 769, 1153, 1721, 1789, 2131, 2339, 2381, 2749, 2777, 3313, 3319, 3517, 3919, 4139, 4337, 4729, 4789, 4903, 4937, 4993, 5171, 5303, 5323, 5507, 5849, 5851, 6271, 6323, 6451, 6959, 6983, 7489, 7919, 8221, 8363, 8419, 9349, 9613, 9619

Offset

1,1

Comments

3313 is the smallest term such that 3313 +- 6 are both prime.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

71 is a term because it is the initial member of 5 consecutive primes {71, 73, 79, 83, 89} and (71 + 73 + 83 + 89)/4 = 79.
271 is a term because it is the initial member of 5 consecutive primes {271, 277, 281, 283, 293} and (271 + 277 + 283 + 293)/4 = 281.

Maple

A293395:= proc(n)local a, b, c, d, e; a:=ithprime(n); b:=ithprime(n+1); c:=ithprime(n+2); d:=ithprime(n+3); e:=ithprime(n+4); if (a + b + d + e)/4 = c then RETURN (a); fi; end: seq(A293395(n), n=1..3000);

Mathematica

Select[Prime@ Range[1200], #[[3]] == Mean@ Delete[#, 3] &@ NestList[NextPrime, #, 4] &] (* Michael De Vlieger, Oct 09 2017 *)

Prog

(PARI) for(n=1, 1000, a=prime(n); b=prime(n+1); c=prime(n+2); d=prime(n+3); e=prime(n+4); if((a+b+d+e)/4==c, print1(a, ", ")));
(PARI) list(lim)=my(v=List(), p=2, q=3, r=5, s=7); forprime(t=11, lim, if(p+q+s+t==4*r, listput(v, p)); p=q; q=r; r=s; s=t); Vec(v) \\ Charles R Greathouse IV, Oct 09 2017

Crossrefs

Cf. A006562, A034964, A122535.

Sequence in context: A142013 A033240 A298103 * A141943 A167441 A349084

Adjacent sequences: A293392 A293393 A293394 * A293396 A293397 A293398

Keyword

nonn

Author

K. D. Bajpai, Oct 08 2017

Extensions

Definiyion simplified by David A. Corneth, Oct 14 2017

Status

approved