A132811 -id:A132811 - cp's OEIS frontend

A132810 Smallest sum of n consecutive odd primes which is a multiple of n.

3, 8, 15, 36, 395, 72, 119, 240, 2349, 300, 539, 276, 923, 714, 435, 496, 629, 702, 2375, 1120, 1995, 1144, 3979, 3192, 3925, 2938, 9531, 1960, 10063, 2670, 3441, 4448, 5907, 6358, 9835, 4464, 5069, 3610, 13533, 4000, 6273, 4410, 21113, 12012, 8325, 8142

Offset: 1

Enoch Haga, Sep 01 2007

			a(5)=395, associated with A132809(5)=71=prime(20) as the first of the 5 consecutive primes, is the smallest sum of 5 consecutive odd primes which is divisible by n=5.

Zak Seidov, Table of n, a(n) for n = 1..1000

Cf. A132809, A132811.

Table[Module[{nn=n,ncop},ncop=Total/@Partition[Prime[Range[2,2500]],nn,1];SelectFirst[ ncop,Mod[#,nn]==0&]],{n,50}] (* Harvey P. Dale, Jan 17 2023 *)

Let A132809(n)=prime(i). Then a(n)= sum(j=i...i+n-1) prime(j). - R. J. Mathar, Nov 27 2007

The example does not match the sequence. Also the offset for all of this bunch of sequences should probably be 1. - N. J. A. Sloane, Sep 13 2007

Edited by R. J. Mathar, Nov 27 2007

A132809 First prime in a sequence of n consecutive odd primes with integral arithmetic mean.

Original entry on oeis.org

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

Enoch Haga, Sep 01 2007

See A054892 for another version.

			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).

Cf. A132810-A132811, A054892.

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

a(n) = {min (prime(k)): sum_{i=0..n-1} prime(k+i) = 0 mod n, k>1 }. - R. J. Mathar, Nov 27 2007

Edited by R. J. Mathar, Nov 27 2007

cp's OEIS Frontend

A132810 Smallest sum of n consecutive odd primes which is a multiple of n.

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