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

2,1

Links

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

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A278300 A034214 A317749 * A227401 A131813 A083038

Adjacent sequences: A253412 A253413 A253414 * A253416 A253417 A253418

Keyword

nonn

Author

Reinhard Zumkeller, Dec 31 2014

Status

approved