A253584 -id:A253584 - cp's OEIS frontend

A253443 Smallest missing number within the first n terms in A109890.

4, 4, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 34, 37, 37, 37, 37, 37

Offset: 4

Reinhard Zumkeller, Jan 01 2015

nonn

A253584(n) occurs exactly A253444(n) times.

Reinhard Zumkeller, Table of n, a(n) for n = 4..10000

Cf. A095258, A095259, A253444 (run lengths), A253584 (range), A253415.

import Data.List (insert)
a253443 n = a253443_list !! (n-4)
a253443_list = f (4, []) 6 where
   f (m,ys) z = g $ dropWhile (< m) $ a027750_row' z where
     g (d:ds) | elem d ys = g ds
              | otherwise = m : f (ins [m, m+1 ..] (insert d ys)) (z + d)
     ins (u:us) vs'@(v:vs) = if u < v then (u, vs') else ins us vs
-- Reinhard Zumkeller, Jan 03 2015

A253444 Lengths of runs of identical terms in A253443.

Original entry on oeis.org

2, 4, 14, 17, 27, 1, 21, 62, 34, 86, 86, 47, 186, 94, 53, 212, 226, 148, 251, 696, 1484, 630, 1870, 563, 813, 188, 1222, 154, 960, 6654, 1980, 8872, 10027, 3628, 5724, 6330, 12059, 10418, 10169, 4192, 4868

Offset: 1

Reinhard Zumkeller, Jan 01 2015

A253584(n) occurs exactly a(n) times in A253443.

Cf. A253443, A253584, A109890.

import Data.List (group)
a253444 n = a253444_list !! (n-1)
a253444_list = map length $ group a253443_list

nn = 2^14; c[_] := False;
Array[Set[{a[#], c[#]}, {#, True}] &, 2]; u = s = a[1] + a[2];
Differences@ Reap[Monitor[Do[k = SelectFirst[Divisors[s], ! c[#] &];
  c[k] = True; s += k;
If[k == u, Sow[n]; While[c[u], u++]], {n, 3, nn}], n] ][[-1, 1]] (* Michael De Vlieger, Apr 27 2024 *)

More terms from Michael De Vlieger, Apr 27 2024

cp's OEIS Frontend

A253443 Smallest missing number within the first n terms in A109890.

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