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A102044 Consider the number m formed from the first n digits of the repeating string 102010201020... Then a(n) = number of prime factors (with repetition) of m. 1
0, 2, 3, 5, 2, 4, 5, 7, 2, 4, 8, 10, 1, 3, 7, 9, 1, 3, 8, 10, 3, 5, 11, 13, 3, 5, 9, 11, 7, 9, 12, 14, 2, 4, 13, 15, 5, 7, 12, 14, 5, 7, 12, 14, 1, 3, 14, 16, 4, 6, 10, 12, 2, 4, 13, 15, 4, 6, 21, 23, 6, 8, 16, 18, 4, 6, 11, 13, 2, 4, 19, 21, 4, 6, 7, 9, 2, 4, 16, 18, 7, 9, 23, 25, 4, 6, 16, 18, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(2n) = a(2n-1)+2.

Consider the number m formed from the first n digits of the repeating string 102010201020... as S(n). Obviously S(2n) = 10*S(2n-1). Also define Repunits (A002275) as R(n) = (10^n-1)/9 = {1, 11, 111, 1111, 11111, ...} and consider a generalized plateau number sequence as X(n) = (34*10^(n+2)-67)/3 = { 1111, 11311, 113311, 1133311, 11333311, ... }. Then S(4n-1) = 34*(10000^n-1)/3333 = 102*R(4n)/R(4) and S(4n+1) = (3400*10000^n-67)/3333 = X(4n)/R(4). - Remarks communicated to Robert G. Wilson v by KAMADA Makoto (m_kamada(AT)nifty.com), Feb 18 2005

LINKS

Table of n, a(n) for n=1..89.

Dario Alejandro Alpern, Factorization using the Elliptic Curve Method.

Makoto Kamada, Factorizations of near-repdigits numbers.

Makoto Kamada, Factorizations of 11...11 (Repunit).

EXAMPLE

a(1) = 0 because 1 is neither prime nor semiprime.

a(2) = 2 because 10 = 2 * 5 is semiprime.

a(3) = 3 because 102 = 2 * 3 * 17, 3 prime factors.

a(4) = 5 because 1020 = 2^2 * 3 * 5 * 17, 5 prime factors with repetition (2 is counted twice because of 2^2 in factorization).

a(5) = 2 because 10201 = 101^2 is a semiprime (and a square) (and a palindrome)

a(6) = 4 because 102010 = 2 * 5 * 101^2

MATHEMATICA

f[n_] := Plus @@ Transpose[ FactorInteger[ IntegerPart[10^(n - 1)*3400 / 3333]]][[2]]; Table[ f[n], {n, 2, 67}] (* Robert G. Wilson v, Feb 14 2005 *)

CROSSREFS

Cf. A004023, A103833.

Sequence in context: A236434 A138182 A167835 * A125766 A093870 A250445

Adjacent sequences:  A102041 A102042 A102043 * A102045 A102046 A102047

KEYWORD

nonn,base

AUTHOR

Jonathan Vos Post, Feb 12 2005

EXTENSIONS

Edited, corrected and extended, a(70)-a(92), by Robert G. Wilson v, Feb 14 2005

Edited by Charles R Greathouse IV, Aug 03 2010

STATUS

approved

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Last modified May 27 11:47 EDT 2022. Contains 354097 sequences. (Running on oeis4.)