A053050 a(n) = smallest integer m such that Sum_{k=1..m} prime(k) is divisible by n.

1, 1, 10, 5, 2, 57, 5, 11, 20, 3, 8, 97, 49, 5, 57, 11, 4, 113, 23, 9, 40, 17, 23, 99, 9, 49, 26, 5, 7, 57, 39, 11, 76, 13, 180, 119, 29, 23, 119, 11, 6, 305, 10, 17, 242, 23, 39, 119, 40, 9, 179, 49, 25, 187, 17, 115, 70, 7, 30, 103, 151, 39, 40, 171, 131, 175, 38, 37, 52, 209, 19

Offset: 1

Author

Felice Russo, Feb 25 2000

Keywords

• easy
• nice
• nonn

Comments

It follows from a theorem of Daniel Shiu that m always exists. See A111287 for details. - N. J. A. Sloane, Nov 05 2005

References

• Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1000 terms from T. D. Noe)
• D. K. L. Shiu, Strings of Congruent Primes, J. Lond. Math. Soc. 61 (2) (2000) 359-373 [MR1760689]

Crossrefs

Cf. A007504, A111287, A002034, A011772.

Cf. A045985, A308749.

Programs

Haskell

a053050 n = head [k | (k, x) <- zip [1..] a007504_list, mod x n == 0]
-- Reinhard Zumkeller, Oct 04 2015, Feb 10 2012

Maple

read transforms; M:=1000; p0:=[seq(ithprime(i),i=1..M)]; q0:=PSUM(p0); w:=[]; for n from 1 to M do p:=n; hit := 0; for i from 1 to M do if q0[i] mod p = 0 then w:=[op(w),i]; hit:=1; break; fi; od: if hit = 0 then break; fi; od: w;

Mathematica

Transpose[With[{aprs=Thread[{Range[500],Accumulate[Prime[Range[ 500]]]}]}, Flatten[Table[ Select[ aprs,Divisible[Last[#],n]&,1],{n,80}],1]]][[1]] (* Harvey P. Dale, Dec 14 2011 *)

Formula

A007504(a(n))/n = A308749(n). - Alois P. Heinz, Jun 21 2019

Extensions

More terms from N. J. A. Sloane, Nov 05 2005