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

1,3

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]

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A007504, A111287, A002034, A011772.

Cf. A045985, A308749.

Sequence in context: A332837 A050020 A050136 * A033330 A214427 A102584

Adjacent sequences: A053047 A053048 A053049 * A053051 A053052 A053053

Keyword

easy,nice,nonn

Author

Felice Russo, Feb 25 2000

Extensions

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

Status

approved