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%I #16 May 29 2022 21:42:43
%S 1,2,5,3,14,8,41,23,4,122,13,68,11,365,38,203,32,1094,113,18,608,6,63,
%T 95,3281,338,53,1823,17,188,284,9842,1013,158,5468,50,563,25,851,
%U 29525,88,3038,28,313,473,16403,149,1688,74,2552,88574,263,9113,7,83,938,1418,49208,446,5063,221,7655,265721,788,27338,20
%N a(n) = A048673(A181815(n)).
%C Maxima are in A007051 and appear at n in A025488, which are the indices of 2^k in A025487. 2^k is idempotent via A181815 but transformed by A003961 to 3^n, which are rendered by A048673 to (3^n + 1)/2.
%C Local minima are in A111333 and appear at n in A098719, which are the indices of P(k) = A002110(k) in A025487. P(k) is transformed by A181815 to p_k = A000040(k), which become p_(k+1) under A003961. Therefore these become (p_(k+1)+1)/2 via A048673.
%H Michael De Vlieger, <a href="/A341351/a341351.png">Annotated logarithmic plot of a(n) for 1 <= n <= A098719(8)</a> accentuating records in red and local minima in blue.
%H Michael De Vlieger, <a href="/A341351/a341351_1.png">log-log plot of a(n) for 1 <= n <= A098719(16)</a>.
%H Michael De Vlieger, <a href="http://www.vincico.com/seq/a341351.html">Notes on this sequence</a>.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) = A048673(A181815(n)).
%F For all n >= 1, A181812(a(n)) = A025487(n).
%t a025487[n_] := {{1}}~Join~Block[{lim = Product[Prime@ i, {i, n}], ww = NestList[Append[#, 1] &, {1}, n - 1]}, Map[Block[{w = #, k = 1}, Sort@ Prepend[If[Length@ # == 0, #, #[[1]]], Product[Prime@ i, {i, Length@ w}]] &@ Reap[Do[If[# < lim, Sow[#]; k = 1, If[k >= Length@ w, Break[], k++]] &@ Apply[Times, MapIndexed[Prime[First@ #2]^#1 &, #]] &@ Set[w, If[k == 1, MapAt[# + 1 &, w, k], PadLeft[#, Length@ w, First@ #] &@ Drop[MapAt[# + Boole[i > 1] &, w, k], k - 1]]], {i, Infinity}]][[-1]] ] &, ww]]; Map[(1 + If[# == 1, 1, Apply[Times, NextPrime[#1]^#2 & @@@ FactorInteger[#]]])/2 &@ Apply[Times, Prime@ Table[LengthWhile[#1, # >= j &], {j, #2}] & @@ {#, Max[#]} &@ If[# == 1, {0}, Function[f, ReplacePart[ConstantArray[0, PrimePi@ f[[-1, 1]] ], #] &@ Map[PrimePi@ First@ # -> Last@ # &, f]]@ FactorInteger@ #]] &, Union@ Flatten@ a025487@ 5] (* _Michael De Vlieger_, Feb 11 2021 *)
%o (PARI) A341351(n) = A048673(A181815(n));
%Y Cf. A002110, A025487, A025488, A048673, A098719, A108951, A111333, A181812, A181815.
%Y Cf. A341352 (inverse).
%Y Cf. A007051 (record values).
%K nonn
%O 1,2
%A _Antti Karttunen_ and _Michael De Vlieger_, Feb 10 2021
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