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
Keywords
Examples
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.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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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);
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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 *)
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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,", ")));
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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
Extensions
Definiyion simplified by David A. Corneth, Oct 14 2017
Examples clarified by Harvey P. Dale, Jul 31 2025
Comments