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A241912 Fixed points of A241916. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

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

FORMULA

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

EXAMPLE

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.

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 *)

PROG

(Scheme, with Antti Karttunen's IntSeq-library)

(define A241912 (FIXED-POINTS 1 1 A241916))

;; Alternatively:

(define (A241912 n) (/ (A242418 (+ n 1)) 2))

CROSSREFS

Complement: A241913.

A079704 is a subsequence.

Cf. A088902, A241916, A242418.

Sequence in context: A090467 A177202 A053868 * A269870 A307824 A081730

Adjacent sequences:  A241909 A241910 A241911 * A241913 A241914 A241915

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 03 2014

STATUS

approved

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)