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Search: id:A102044
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| A102044 |
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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. |
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2
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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.
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LINKS
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Dario Alejandro Alpern, Factorization using the Elliptic Curve Method.
Makoto Kamada, Factorizations of near-repdigits numbers.
Makoto Kamada, Factorizations of 11...11 (Repunit).
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EXAMPLE
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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
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MATHEMATICA
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f[n_] := Plus @@ Transpose[ FactorInteger[ IntegerPart[10^(n - 1)*3400 / 3333]]][[2]]; Table[ f[n], {n, 2, 67}] (from Robert G. Wilson v Feb 14 2005)
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CROSSREFS
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Cf. A004023, A103833.
Sequence in context: A133907 A060084 A138182 this_sequence A125766 A093870 A126833
Adjacent sequences: A102041 A102042 A102043 this_sequence A102045 A102046 A102047
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 12 2005
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EXTENSIONS
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Edited, corrected and extended, a(70) - a(92), by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 14 2005
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