A132809 First prime in a sequence of n consecutive odd primes with integral arithmetic mean.
3, 3, 5, 71, 5, 7, 17, 239, 13, 29, 5, 43, 23, 5, 5, 7, 7, 79, 17, 47, 11, 109, 73, 97, 53, 271, 13, 263, 23, 41, 61, 97, 101, 181, 41, 47, 13, 233, 13, 53, 13, 359, 151, 71, 61, 239, 73, 443, 859, 29, 131, 131, 61, 313, 101, 19, 151, 521, 3, 571, 31, 7, 79, 109, 97, 53, 53
Offset: 2
Examples
For n=2 we add prime(2)+prime(3)=3+5=8 which is already a multiple of n=2, so we add the first of the primes, 3, at a(n=2). For n=5 we test 3+5+7+11+13=39 against being a multiple of n=5, then 5+7+11+13+17=53, then 7+11+13+17+19=67 etc. and find that 71+73+79+83+89=395 is a multiple. We place the smallest member in this sequence of 5 primes, 71, at a(n=5).
Programs
-
Maple
A132809 := proc(n) local i,j ; for i from 2 do if add( ithprime(i+j),j=0..n-1) mod n = 0 then RETURN(ithprime(i)) ; fi ; od: end: seq(A132809(n),n=2..80) ; # R. J. Mathar, Nov 27 2007
Formula
a(n) = {min (prime(k)): sum_{i=0..n-1} prime(k+i) = 0 mod n, k>1 }. - R. J. Mathar, Nov 27 2007
Extensions
Edited by R. J. Mathar, Nov 27 2007
Comments