A120249 -id:A120249 - cp's OEIS frontend

A120251 A120249[n] modulo A120250[n].

0, 0, 1, 0, 2, 1, 3, 0, 1, 2, 5, 1, 8, 3, 2, 0, 13, 1, 21, 2, 3, 5, 34, 1, 3, 8, 1, 3, 55, 2, 89, 0, 5, 13, 5, 1, 144, 21, 8, 2, 233, 3, 377, 5, 2, 34, 610, 1, 4, 3, 13, 8, 987, 1, 8, 3, 21, 55, 1597, 2, 2584, 89, 3, 0, 13, 5, 4181, 13, 34, 5, 6765, 1, 10946, 144, 3, 21, 7, 8, 17711, 2

Offset: 1

Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 12 2006

a[n] = 0 precisely when n is a power of 2.

			a[n] = A120249[2646] modulo A120250[2646] = 42 modulo 19 = 4

Cf. Corresponding denominators in A120250.

Table[If[n == 1, 0, (fl = FactorInteger[n]; pq = Table[1, {i, 1, PrimePi[Last[fl][[1]]]}]; While[Length[fl] > 0, pp = First[fl]; fl = Drop[fl, 1]; pq[[PrimePi[pp[[1]]]]] = pp[[2]] + 1;]; Mod[Numerator[FromContinuedFraction[pq]], Denominator[FromContinuedFraction[pq]]])], {n, 1, 80}]

a[n] = Mod[A120249[n], A120250[n]]

A120250 Denominator of cfenc(n) (see definition in comments).

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 5, 1, 3, 3, 8, 2, 13, 5, 5, 1, 21, 3, 34, 3, 8, 8, 55, 2, 4, 13, 4, 5, 89, 5, 144, 1, 13, 21, 7, 3, 233, 34, 21, 3, 377, 8, 610, 8, 7, 55, 987, 2, 7, 4, 34, 13, 1597, 4, 11, 5, 55, 89, 2584, 5, 4181, 144, 11, 1, 18, 13, 6765, 21, 89, 7, 10946, 3, 17711, 233, 7, 34

Offset: 1

Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 12 2006

a(n) := denominator of cfenc(n). cfenc(n) := number given by interpreting as a continued fraction expansion (indexed from 1) the sequence whose i-th entry is one plus the exponent on the i-th prime factor of n (fix cfenc(1)=1).

			a(2646) = denominator(cfenc(2646)) = denominator(cfenc(2^1 * 3^3 * 7^2)) = denominator(FromContinuedFraction[{2; 4, 1, 3}]) = denominator(2 + 1/(4 + 1/(1 + 1/3))) = denominator(42/19) = 19.

Hans Havermann, Table of n, a(n) for n = 1..10000

Corresponding numerators in A120249. Numerators modulo respective denominators in A120251.

Table[If[n == 1, 1, (fl = FactorInteger[n]; pq = Table[1, {i, 1, PrimePi[Last[fl][[1]]]}]; While[Length[fl] > 0, pp = First[fl]; fl = Drop[fl, 1]; pq[[PrimePi[pp[[1]]]]] = pp[[2]] + 1;]; Denominator[FromContinuedFraction[pq]])],{n,1,80}]

a(2^k) = 1.

a(prime(n)) = Fibonacci(n+1).

cp's OEIS Frontend

A120251 A120249[n] modulo A120250[n].

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