A139476 -id:A139476 - cp's OEIS frontend

A139474 a(n) = ((2sqrt(2) + 3)^(2^(prime(n) - 1) - 1) - (3 - 2sqrt(2))^(2^(prime(n) - 1) - 1))/(4*sqrt(2)).

1, 35, 53789260175, 300027707381709879256191290532493317737977820735

Offset: 1

Artur Jasinski, Apr 22 2008

nonn

Next term a(5) has 783 decimal digits.

Conjecture of Kenneth J Ramsey from May 16 2006 (see A001109): a(n) is divisible by 2^prime(n)-1 if and only 2^prime(n)-1 is a Mersenne prime.

Cf. A001109, A139474, A139475, A139476.

Table[Expand[((2*Sqrt[2] + 3)^(2^(Prime[n] - 1) - 1) - (3 - 2*Sqrt[2])^(2^(Prime[n] - 1) - 1))/(4*Sqrt[2])], {n, 1, 10}]

A139475 Number of digits in the decimal expansion of A139474(n).

Original entry on oeis.org

1, 2, 11, 48, 783, 3135, 50170

Offset: 1

Artur Jasinski, Apr 22 2008, Sep 29 2008

Cf. A001109, A055642, A139473, A139474, A139476.

Table[Length[IntegerDigits[Expand[((2*Sqrt[2] + 3)^(2^(Prime[n] - 1) - 1) - (3 - 2*Sqrt[2])^(2^(Prime[n] - 1) - 1))/(4*Sqrt[2])]]], {n, 1, 6}]

a(n) = A055642(A139474(n)). - Amiram Eldar, Oct 13 2024

a(7) from Amiram Eldar, Oct 13 2024

A139473 a(n)=((2Sqrt[2] + 3)^(2^(n - 1) - 1) - (3 - 2Sqrt[2])^(2^(n - 1) - 1))/(4*Sqrt[2]).

Original entry on oeis.org

0, 1, 35, 40391, 53789260175, 95393218491883573553951, 300027707381709879256191290532493317737977820735

Offset: 1

Artur Jasinski, Apr 22 2008

nonn

Cf. A001109, A139474, A139475, A139476.

Table[Expand[((2*Sqrt[2] + 3)^(2^(n - 1) - 1) - (3 - 2*Sqrt[2])^(2^(n - 1) - 1))/(4*Sqrt[2])], {n, 1, 10}] (*Artur Jasinski*)

A139478 a(n) = A001109(n) in binary.

Original entry on oeis.org

1, 110, 100011, 11001100, 10010100101, 1101100010010, 1001110111000111, 111001011110011000, 101001110111111001001, 11110100000011100011110, 10110001110011101011101011, 10000001100010101101001100100

Offset: 1

Artur Jasinski, Apr 22 2008

Cf. A001109, A139473, A139474, A139475, A139476, A139478.

a = {}; Do[k = IntegerDigits[Expand[((2*Sqrt[2] + 3)^(n) - (3 - 2*Sqrt[2])^(n))/(4*Sqrt[2])], 2]; AppendTo[a, FromDigits[k]], {n, 1, 50}]; a (*Artur Jasinski*)

A139477 Number of binary digits in A001109(n).

Original entry on oeis.org

1, 1, 3, 6, 8, 11, 13, 16, 18, 21, 23, 26, 29, 31, 34, 36, 39, 41, 44, 46, 49, 51, 54, 56, 59, 62, 64, 67, 69, 72, 74, 77, 79, 82, 84, 87, 90, 92, 95, 97, 100, 102, 105, 107, 110, 112, 115, 118, 120, 123, 125, 128, 130, 133, 135, 138, 140, 143, 146, 148, 151, 153, 156, 158, 161, 163, 166, 168

Offset: 0

Artur Jasinski, Apr 22 2008

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A001109, A139473, A139474, A139475, A139476, A139478.

a[0]:= 0: a[1]:= 1: R[0]:= 1: R[1]:= 1:
for n from 2 to 100 do
   a[n]:=  6*a[n-1] - a[n-2];
   R[n]:= ilog2(a[n])+1;
od:
seq(R[i],i=0..100); # Robert Israel, Nov 23 2024

a = {}; Do[k = Length[IntegerDigits[Expand[((2*Sqrt[2] + 3)^(n) - (3 - 2*Sqrt[2])^(n))/(4*Sqrt[2])], 2]]; Print[k]; AppendTo[a, k], {n, 1, 50}]; a
Rest[IntegerLength[#,2]&/@LinearRecurrence[{6,-1},{0,1},60]] (* Harvey P. Dale, Feb 11 2015 *)

a(n) = A070939(A001109(n)). - Michel Marcus, Nov 02 2013

Incorrect link to index entries for linear recurrences with constant coefficients removed by Colin Barker, Oct 13 2015

a(0) = 1 prepended and more terms by Robert Israel, Nov 23 2024

A140418 Position of cubes in the EKG sequence (A064413).

Original entry on oeis.org

1, 8, 22, 64, 112, 199, 319, 485, 696, 958, 1279, 1649, 2090, 2612, 3241, 3932, 4733, 5608, 6583, 7707, 8926

Offset: 1

Parthasarathy Nambi, Jun 17 2008

nonn

The squares (A139476), primes (A064955) and cubes (this sequence) all appear in increasing order. Is this true for all other powers also?

			The position of 3^3 is 22.
The position of 5^3 is 112.

Cf. A064413, A064955, A139476.

cp's OEIS Frontend

A139474 a(n) = ((2*sqrt(2) + 3)^(2^(prime(n) - 1) - 1) - (3 - 2*sqrt(2))^(2^(prime(n) - 1) - 1))/(4*sqrt(2)).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A139475 Number of digits in the decimal expansion of A139474(n).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

Extensions

A139473 a(n)=((2*Sqrt[2] + 3)^(2^(n - 1) - 1) - (3 - 2*Sqrt[2])^(2^(n - 1) - 1))/(4*Sqrt[2]).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A139478 a(n) = A001109(n) in binary.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

A139477 Number of binary digits in A001109(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A140418 Position of cubes in the EKG sequence (A064413).

Views

Author

Keywords

Comments

Examples

Crossrefs

A139474 a(n) = ((2sqrt(2) + 3)^(2^(prime(n) - 1) - 1) - (3 - 2sqrt(2))^(2^(prime(n) - 1) - 1))/(4*sqrt(2)).

A139473 a(n)=((2Sqrt[2] + 3)^(2^(n - 1) - 1) - (3 - 2Sqrt[2])^(2^(n - 1) - 1))/(4*Sqrt[2]).