A253415 Smallest missing number within the first n terms in A095258.

2, 4, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 22, 22, 22, 22, 22, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31

Offset: 2

Author

Reinhard Zumkeller, Dec 31 2014

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 2..10000 (terms 2..797 from Reinhard Zumkeller)

Crossrefs

Cf. A095258, A095259, A253425 (run lengths).

Programs

Haskell

import Data.List (delete)
a253415 n = a253415_list !! (n-2)
a253415_list = f [2..] 1 where
   f xs z = g xs where
     g (y:ys) = if mod z' y > 0 then g ys else x : f xs' (z + y)
                where xs'@(x:_) = delete y xs
     z' = z + 2
-- Reinhard Zumkeller, Dec 31 2014

Mathematica

c[] = 0; c[1] = j = 1; u = 2; s = 3; Reap[Do[d = Divisors[s]; k = 1; While[c[d[[k]]] > 0, k++]; Set[k, d[[k]]]; Set[c[k], i]; If[k == u, While[c[u] > 0, u++]]; Sow[u]; j = k; s += k, {i, 2, 2^12}]][[-1, -1]] (* _Michael De Vlieger, Jan 23 2022 *)

Python

from itertools import islice
from sympy import divisors
def A253415_gen(): # generator of terms, first term is a(2)
    bset, m, s = {1}, 2, 3
    while True:
        for d in divisors(s):
            if d not in bset:
                bset.add(d)
                while m in bset:
                    m += 1
                yield m
                s += d
                break
A253415_list = list(islice(A253415_gen(),30)) # Chai Wah Wu, Jan 25 2022