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A347355 Index of first n in A347354.

%I A347355 #16 May 24 2023 22:29:32
%S A347355 1,2,4,5,8,10,13,18,23,24,27,32,35,39,40,50,53,54,62,67,70,73,85,89,
%T A347355 94,99,100,104,105,115,129,132,134,140,143,153,157,159,170,173,175,
%U A347355 180,184,188,192,194,199,229,233,235,238,248,249,254,267,275,283,289,294
%N A347355 Index of first n in A347354.
%C A347355 Indices of records in A347354, where the record is A000027(n).
%C A347355 List of k such that A089576(k) = A089576(k-1) + 1.
%H A347355 Michael De Vlieger, <a href="/A347355/b347355.txt">Table of n, a(n) for n = 1..5587</a>
%e A347355 Relation of A347354 and irregular triangle A347285, placing "." after the last term in the current row where T(n,k) exceeds T(n-1,k). Since the rows of A347285 reach a fixed point of 0, we interpret T(n,k) for vacant T(n-1,k) as exceeding same. The indices n that are highlighted with parentheses are the terms in this sequence.
%e A347355     n     Row n of A347285     A347354(n)
%e A347355    --------------------------------------
%e A347355     0:    0
%e A347355    (1):   1.                   1
%e A347355    (2):   2  1.                2
%e A347355     3:    3. 1                 1
%e A347355    (4):   4  2  1.             3
%e A347355    (5):   5  3  2  1.          4
%e A347355     6:    6. 3  2  1           1
%e A347355     7:    7  4. 2  1           2
%e A347355    (8):   8  5  3  2  1.       5
%e A347355     9:    9. 5  3  2  1        1
%e A347355   (10):  10  6  4  3  2  1.    6
%e A347355   ...
%t A347355 Block[{nn = 300, a = {1}, c, e, m}, e[1] = 0; Do[c = 1; e[1]++; Do[Set[m, j]; Which[e[j - 1] == 1, Break[], IntegerQ@ e[j], If[e[j] < #, e[j]++; c++] &@ Floor@ Log[Prime[j], Prime[j - 1]^e[j - 1]], True, Set[e[j], 1]], {j, 2, k}]; If[c == m - 2, AppendTo[a, k - 1]], {k, 2, nn}]; Delete[a, {3}]]
%Y A347355 Cf. A089576, A347285, A347354.
%K A347355 nonn,easy
%O A347355 1,2
%A A347355 _Michael De Vlieger_, Sep 28 2021