A341351 a(n) = A048673(A181815(n)).

1, 2, 5, 3, 14, 8, 41, 23, 4, 122, 13, 68, 11, 365, 38, 203, 32, 1094, 113, 18, 608, 6, 63, 95, 3281, 338, 53, 1823, 17, 188, 284, 9842, 1013, 158, 5468, 50, 563, 25, 851, 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

Offset: 1

Author

Antti Karttunen and Michael De Vlieger, Feb 10 2021

Keywords

• nonn

Comments

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.

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.

Links

• Michael De Vlieger, Annotated logarithmic plot of a(n) for 1 <= n <= A098719(8) accentuating records in red and local minima in blue.
• Michael De Vlieger, log-log plot of a(n) for 1 <= n <= A098719(16).
• Michael De Vlieger, Notes on this sequence.
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A002110, A025487, A025488, A048673, A098719, A108951, A111333, A181812, A181815.

Cf. A341352 (inverse).

Cf. A007051 (record values).

Programs

Mathematica

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 *)

PARI

A341351(n) = A048673(A181815(n));

Formula

a(n) = A048673(A181815(n)).

For all n >= 1, A181812(a(n)) = A025487(n).