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A330818 Numbers of the form 2^(2*p+1), where p is a Mersenne exponent, A000043. 7
32, 128, 2048, 32768, 134217728, 34359738368, 549755813888, 9223372036854775808, 10633823966279326983230456482242756608, 766247770432944429179173513575154591809369561091801088 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also the first factor of A330817, 2^(2*p+1)*M_p^2. The second factor of A330817 is A133049.

LINKS

Walter Kehowski, Table of n, a(n) for n = 1..12

FORMULA

a(n) = 2^(2*A000043(n)+1).

EXAMPLE

a(1) = 2^(2*2+1) = 32. Since M_2=3, the number 2^5*3^2 has power-spectral basis {225,64}.

MAPLE

A330818:=[]:

for www to 1 do

for i from 1 to 31 do

  #ithprime(31)=127

  p:=ithprime(i);

  q:=2^p-1;

  if isprime(q) then x:=2^(2*p+1); A330818:=[op(A330818), x]; fi;

od;

od;

A330818;

MATHEMATICA

2^(2 * MersennePrimeExponent[Range[10]] + 1) (* Amiram Eldar, Jan 03 2020 *)

CROSSREFS

Cf. A000043, A000668, A132794, A133049, A330817, A330819, A330820.

Sequence in context: A033323 A091905 A100626 * A231045 A031447 A153074

Adjacent sequences:  A330815 A330816 A330817 * A330819 A330820 A330821

KEYWORD

nonn

AUTHOR

Walter Kehowski, Jan 01 2020

STATUS

approved

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Last modified March 2 09:56 EST 2021. Contains 341746 sequences. (Running on oeis4.)