A290389 Inverse to A290308.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 3, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 9, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 27, 268435456, 536870912, 1073741824, 2147483648, 4294967296

Offset: 0

Author

Rémy Sigrist, Jul 29 2017

Keywords

• nonn
• base

Comments

The sequence n -> a(n-1) (with n > 0) is an analog of A005940 for the decimal base.

a(A052382(k) * 10^(n-1)) = prime(n)^k for any n > 0 and k > 0 (where prime(n) is the n-th prime).

Examples

			A290308(1) = 0, hence a(0) = 1.
A290308(2) = 1, hence a(1) = 2.
A290308(3) = 10, hence a(10) = 3.
A290308(4) = 2, hence a(2) = 4.
A290308(5) = 100, hence a(100) = 5.
A290308(6) = 101, hence a(101) = 6.
A290308(7) = 1000, hence a(1000) = 7.
A290308(8) = 3, hence a(3) = 8.
A290308(9) = 20, hence a(20) = 9.
A290308(10) = 1001, hence a(1001) = 10.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..2500
• Rémy Sigrist, PARI program for A290389
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A005940, A290308.

Programs

Mathematica

f[n_] := Function[m, Sum[(1 + Mod[Floor[(8 n + 1 - 9^m)/(8*9^j)], 9]) 10^j, {j, 0, m - 1}]]@ Floor@ Log[9, 8 n + 1]; Block[{nn = 35, s},s = Association@ Array[f@ # -> # &, nn]; {1}~Join~Table[Times @@ MapIndexed[Prime[First[#2]]^#1 &, If[DigitCount[n, 10, 0] > 0, Function[t, Reverse@ Flatten@ Apply[Join, {SplitBy[Take[Reverse@ t, Length@ t - Length@ #],0] /. z_List /; First@ z == 0 :> Most@ z, #}] &@ TakeWhile[t, # == 0 &]]@ Reverse@ IntegerDigits[n], {Lookup[s, n]}]], {n, nn}]] (* Michael De Vlieger, Jul 31 2017 *)

PARI

See Links section.