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

2,1

Comments

See A054892 for another version.

Links

Table of n, a(n) for n=2..68.

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

Example

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).

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

Crossrefs

Cf. A132810-A132811, A054892.

Sequence in context: A280779 A241591 A248592 * A265960 A279062 A367763

Adjacent sequences: A132806 A132807 A132808 * A132810 A132811 A132812

Keyword

easy,nonn

Author

Enoch Haga, Sep 01 2007

Extensions

Edited by R. J. Mathar, Nov 27 2007

Status

approved