VOOZH about

URL: https://oeis.org/A293395

⇱ A293395 - OEIS

login
A293395
The initial member of 5 consecutive primes whose arithmetic mean is the middle member.
4
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 + 79 + 83 + 89)/5 = 79.
271 is a term because it is the initial member of 5 consecutive primes {271, 277, 281, 283, 293} and (271 + 277 + 281 + 283 + 293)/5 = 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 *)
Select[Partition[Prime[Range[1200]], 5, 1], Mean[#]==#[[3]]&][[;; , 1]] (* Harvey P. Dale, Jul 31 2025 *)
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
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Oct 08 2017
EXTENSIONS
Definiyion simplified by David A. Corneth, Oct 14 2017
Examples clarified by Harvey P. Dale, Jul 31 2025
STATUS
approved