A387921 - OEIS

A387921

a(n) is the least number k such that A005704(k) is divisible by prime(n).

1, 2, 3, 4, 11, 20, 49, 29, 9, 34, 18, 109, 32, 69, 13, 45, 90, 77, 33, 182, 183, 59, 446, 167, 101, 56, 206, 125, 63, 46, 36, 28, 37, 130, 301, 174, 185, 236, 104, 99, 136, 578, 78, 391, 86, 79, 200, 177, 241, 64, 547, 27, 444, 337, 115, 61, 194, 372, 117, 464

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OFFSET

1,2

COMMENTS

a(n) exists for all n (Woodrow, 2004).

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

R. E. Woodrow, 40th International Mathematical Olympiad, Vietnam Team Selection Test, Hanoi, Vietnam, May 8-9, 2001, The Olympiad Corner No. 235, Crux Mathematicorum, Vol. 30, No. 1 (2004), p. 17.

EXAMPLE

a(1) = 1 since A005704(1) = 2 is the least term of A005704 that is divisible by prime(1) = 2.

a(5) = 11 since A005704(11) = 33 is the least term of A005704 that is divisible by prime(5) = 11.

MATHEMATICA

s[0] = 1; s[n_] := s[n] = s[n-1] + s[Floor[n/3]]; a[n_] := Module[{p = Prime[n], k = 1}, While[!Divisible[s[k], p], k++]; k]; Array[a, 100]

PROG

(PARI) memoA005704 = Map();

s(n) = {my(v); if(!mapisdefined(memoA005704, n, &v), v = if(n == 0, 1, s(n-1) + s(n\3)); mapput(memoA005704, n, v)); v; }

a(n) = {my(p = prime(n), k = 1); while(s(k) % p, k++); k; }

CROSSREFS

Cf. A005704.

Sequence in context: A297180 A162969 A104109 * A066347 A367807 A118596

Adjacent sequences: A387918 A387919 A387920 * A387922 A387923 A387924

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 12 2025

STATUS

approved