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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 + 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
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Oct 08 2017
EXTENSIONS
Definiyion simplified by David A. Corneth, Oct 14 2017
STATUS
approved