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A053050 a(n) = smallest integer m such that Sum_{k=1..m} prime(k) is divisible by n. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 2 09:22 EDT 2021. Contains 346422 sequences. (Running on oeis4.)