

A054892


Smallest prime a(n) such that the sum of n consecutive primes starting with a(n) is divisible by n.


5



2, 3, 3, 5, 71, 5, 7, 17, 239, 13, 29, 5, 43, 23, 5, 5, 7, 7, 79, 17, 47, 11, 2, 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, 2, 61, 313, 101, 19, 151, 521, 3, 571, 31, 7, 79, 109, 97, 53
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OFFSET

1,1


COMMENTS

See A132809 for another version.
In some cases (n=1,2,25,..), like a(25)=97, the sum of 25 consecutive primes starts with the 25th prime and is divided by 25: Sum=97+...+227=3925=25*157


LINKS

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


FORMULA

Min[q_1; Sum[q_i; {i, 1, n}]]=n*X], q_i is a prime (rarely only q_i=Prime[i])


EXAMPLE

a(8) = 17 since the sum of the 8 consecutive primes starting with 17 is 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 = 240, which is divisible by 8. No prime less than 17 has this property: for example, 7 + 11 + ... + 31 = 150 which is not divisible by 8.


MATHEMATICA

f[n_] := Block[{k = 1, t}, While[t = Table[Prime[i], {i, k, k + n  1}]; Mod[Plus @@ t, n] > 0, k++ ]; t]; First /@ Table[f[n], {n, 67}] (* Ray Chandler, Oct 09 2006 *)


CROSSREFS

Cf. A054643, A024672, A034961, A077388, A077389, A122820, A132809.
Sequence in context: A154646 A046826 A323713 * A104570 A071915 A182578
Adjacent sequences: A054889 A054890 A054891 * A054893 A054894 A054895


KEYWORD

nonn


AUTHOR

Labos Elemer, May 23 2000


STATUS

approved



