A146215 a(1) = 1, a(n+1) = a(n) + mod(a(n), p), where p is the lowest prime such that mod(a(n), p) is nonzero.

1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 14, 16, 17, 18, 21, 22, 23, 24, 28, 29, 30, 32, 34, 35, 36, 37, 38, 40, 41, 42, 44, 46, 47, 48, 51, 52, 53, 54, 58, 59, 60, 64, 65, 66, 67, 68, 70, 71, 72, 74, 76, 77, 78, 81, 82, 83, 84, 88, 89, 90, 96, 97, 98, 100, 101, 102

Offset

1,2

Comments

Former name: Addition of lowest nonzero prime division remainders.

The sequence is linear on a large scale. For 10^9 terms, a(n)/n is calculated to be 1.5859351, giving an approximate natural density of 0.6305428.

Links

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

Mathematica

lp[n_]:=Module[{t=2}, While[Mod[n, t]==0, t=NextPrime[t]]; t]; NestList[ #+Mod[#, lp[#]]&, 1, 70] (* Harvey P. Dale, Jul 19 2013 *)

Prog

(MATLAB) % prime is expected to be an array containing all required primes.
a = zeros(1, terms); a(1) = 1; for n = 1:terms-1 j = 1; right = 0; while (right == 0) if (mod(a(n), prime(j)) == 0) j = j + 1; else right = 1; end end a(n+1) = a(n) + mod(a(n), prime(j)); end

Crossrefs

Sequence in context: A249031 A085302 A193928 * A086743 A285432 A039079

Adjacent sequences: A146212 A146213 A146214 * A146216 A146217 A146218

Keyword

easy,nonn

Author

Sigurd Wenner (sigurd.wenner(AT)ils.uio.no), Oct 28 2008

Extensions

Corrected and extended by Harvey P. Dale, Jul 19 2013

Status

approved