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A342594 Earliest occurrence of the next distinct width pattern (as listed in A342592) in the symmetric representation of sigma(n) not yet encountered as n increases. 4
1, 3, 6, 9, 15, 18, 21, 30, 45, 60, 63, 72, 75, 78, 81, 90, 105, 120, 135, 147, 150, 162, 165, 180, 189, 210, 225, 231, 300, 315, 357, 360, 378, 390, 405, 420, 441, 450, 465, 495, 504, 525, 540, 567, 630, 648, 666, 675, 690, 693, 729, 735, 770, 810, 825, 840, 855, 858, 882, 900, 903, 945, 975, 990 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The width pattern of the symmetric representation of sigma(a(n)) is the n-th row of the table of A342592.

Conjecture: If for some number n the symmetric representation of sigma(n) has the symmetric width pattern w in row n of A342592 then infinitely many numbers have that width pattern w.

LINKS

Table of n, a(n) for n=1..64.

EXAMPLE

a(1) = 1 is the smallest power of 2 whose symmetric representation of sigma has width pattern (1).

a(2) = 3 is the smallest odd prime whose symmetric representation of sigma has width pattern (1 0 1).

a(4) = 9 is the first number whose symmetric representation of sigma has width pattern (1 0 1 0 1). The infinitely many numbers 2^s * p^2, s >= 0 and p an odd prime larger than 2^(s+1), have the same width pattern.

MATHEMATICA

(* function a341969[ ] is defined in A341969 *)

a342594[n_] := Module[{listW={}, listK={}, k, w}, For[k=1, k<=n, k++, w=a341969[k]; If[!MemberQ[listW, w], AppendTo[listW, w]; AppendTo[listK, k]]]; listK]

a342594[990] (* 64 entries; the 64th new pattern is encountered at n=990 *)

CROSSREFS

Cf. A235791, A237048, A237270, A237591, A237593, A249223, As341969, A342592.

Sequence in context: A058597 A310175 A146562 * A179893 A274191 A133331

Adjacent sequences:  A342591 A342592 A342593 * A342595 A342596 A342597

KEYWORD

nonn

AUTHOR

Hartmut F. W. Hoft, Mar 16 2021

STATUS

approved

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Last modified May 26 07:48 EDT 2022. Contains 354077 sequences. (Running on oeis4.)