A054892 Smallest prime a(n) such that the sum of n consecutive primes starting with a(n) is divisible by n.
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
Offset: 1
Keywords
Examples
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.
Links
- Zak Seidov, Table of n, a(n) for n = 1..1000
Programs
-
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 *) Module[{prs=Prime[Range[250]]},Table[SelectFirst[Partition[prs,n,1],Mod[Total[#],n]==0&],{n,70}]][[;;,1]] (* Harvey P. Dale, Jul 11 2023 *)
Formula
a(n) = min{q_1 | Sum_{i=1..n} q_i = n*X}, q_i is a prime (rarely only a(n) = prime(n)).
Comments