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

1,2

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

Table of n, a(n) for n=1..66.

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

Formula

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

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

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 *)

Prog

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

Crossrefs

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

Cf. A341352 (inverse).

Cf. A007051 (record values).

Sequence in context: A267101 A035334 A243506 * A285742 A245612 A243066

Adjacent sequences: A341348 A341349 A341350 * A341352 A341353 A341354

Keyword

nonn

Author

Antti Karttunen and Michael De Vlieger, Feb 10 2021

Status

approved