A241912 Fixed points of A241916.

1, 2, 3, 4, 5, 7, 8, 11, 13, 15, 16, 17, 18, 19, 23, 29, 31, 32, 37, 41, 43, 45, 47, 50, 53, 55, 59, 61, 64, 67, 71, 73, 79, 83, 89, 97, 98, 101, 103, 105, 107, 108, 109, 113, 119, 127, 128, 131, 135, 137, 139, 149, 150, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

Offset: 1

Author

Antti Karttunen, May 03 2014

Keywords

• nonn

Comments

A natural number n occurs here if and only if it is either a power of 2, or satisfies A001511(n) = A071178(n) [the exponent of highest power of 2 dividing n is one less than the exponent of the largest prime factor of n], and all the intermediate exponents form a palindrome. [Please see the definition of A241916.]

Numbers for which the corresponding rows in A112798 and A241918 are the conjugate partitions of each other.

Examples

			98 = 2*7*7 = p_1^1 * p_2^0 * p_3^0 * p_4^2 is included because 2 occurs once, the highest prime factor 7 occurs twice (thus A001511(150) = A071178(150) = 2), and the intermediate exponents (in this case {0,0}) form a palindrome.
150 = 2*3*5*5 = p_1^1 * p_2^1 * p_3^2 is included because 2 occurs once, the highest prime factor 5 occurs twice (thus A001511(150) = A071178(150) = 2), and the intermediate exponents (in this case 1) form a palindrome.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4931

Crossrefs

Complement: A241913.

A079704 is a subsequence.

Cf. A088902, A241916, A242418.

Programs

Mathematica

f[n_] := If[n == 1, {0}, Function[f, ReplacePart[Table[0, {PrimePi[f[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> Last@ # &, f]]@ FactorInteger@ n]; g[w_List] := Times @@ Flatten@ MapIndexed[Prime[#2]^#1 &, w]; Table[#[[n + 1]]/2, {n, Length@ # - 1}] &@ Select[Range@ 400, g@ f@ # == g@ Reverse@ f@ # &] (* Michael De Vlieger, Aug 27 2016 *)

Formula

a(n) = A242418(n+1)/2.