A119408 -id:A119408 - cp's OEIS frontend

A128889 a(n) = (2^(n^2) - 1)/(2^n - 1).

1, 5, 73, 4369, 1082401, 1090785345, 4432676798593, 72340172838076673, 4731607904558235517441, 1239150146850664126585242625, 1298708349570020393652962442872833, 5445847423328601499764522166702896582657, 91355004067076339167413824240109498970069278721

Offset: 1

Leroy Quet, Apr 19 2007

nonn

a(n) is prime for n in A156585. Conjecture: gpf(a(n)) = gpf(Phi(n,2^n)), where Phi(n,2^n) = A070526(n). - Thomas Ordowski, Feb 16 2014

The conjecture fails at n = 26, where 3340762283952395329506327023033 > 215656329382891550920192462661. Next counterexample for n = 30, but no odd counterexamples found so far. - Charles R Greathouse IV, Feb 17 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..50

Cf. A051156, A119408, A156585.

a:=n->(2^(n^2)-1)/(2^n-1): seq(a(n),n=1..13);

f[n_] := (2^(n^2) - 1)/(2^n - 1); Array[f, 12]
F[n_] := Plus @@ Table[2^((n - i)*n), {i, 1, n}] (* Enrique Pérez Herrero, Feb 23 2009 *)
Table[(2^(n^2) - 1)/(2^n - 1), {n, 1, 20}] (* Vincenzo Librandi, Feb 18 2014 *)

a(n)=(2^n^2-1)/(2^n-1) \\ Charles R Greathouse IV, Feb 17 2014

a(n) = Sum_{k=1..n} 2^((n-k)*n). - Enrique Pérez Herrero, Feb 23 2009

More terms from Robert G. Wilson v and Emeric Deutsch, Apr 22 2007

A256275 Decimal equivalent of the binary string generated by the negation of the n X n identity matrix.

Original entry on oeis.org

0, 6, 238, 31710, 16510910, 34089189246, 280371153272574, 9205322385119247870, 1207744073945406663293950, 633515663914742881158342637566, 1328903397983747395279166325955489790, 11149011303623843458013522930838119932485630, 374121581799746201009538413109130562019709006364670

Offset: 1

Stuart Bruff, Jun 02 2015

nonn

			For n = 3, a(3) = 2^(3^2) - (1 + (2^((3+1)*(3-1)) + 2^((3+1)*(3-2)) + 2^((3+1)*(3-3)))) = 2^9  - (1 + (2^8 + 2^4 + 2^0)) = 512 - (1 + (256 + 16 + 1)) = 512 - 274 = 238.

Stuart Bruff, Table of n, a(n) for n = 1..26

Cf. A119408.

[(2^(n^2)-2)*(1-2^n)/(1-2^(n+1)): n in [1..15]]; // Vincenzo Librandi, Jun 03 2015

seq((2^(n^2)-2)*(1-2^n)/(1-2^(n+1)),n=1..26); # Robert Israel, Jun 02 2015

2^(n^2) - (1 + Summation[k=1..n (2^((n+1).(n-k)))])

Table[2^(n^2) - (1 + Sum[2^((n + 1) (n - k)), {k, n}]), {n, 12}] (* Michael De Vlieger, Jun 02 2015 *)

a(n) = 2^(n^2) - (1 + (2^((n+1)*(n-1)) + 2^((n+1)*(n-2) + .. 1))).
a(n) = 2^(n^2) - (1 + A119408(n)).
a(n) = ((2^(n^2) - 2)*(2^n - 1))/(2*2^n - 1)

cp's OEIS Frontend

A128889 a(n) = (2^(n^2) - 1)/(2^n - 1).

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