A073019 Numbers n such that the absolute value of the real part of (1+2*I)^n is prime.

2, 3, 4, 5, 7, 11, 13, 17, 19, 89, 163, 167, 233, 251, 349, 401, 757, 1423, 3049, 3643, 11987, 19801, 26393, 32303, 35363, 35863, 36607, 36683

Offset

1,1

Comments

In the first 28 terms only n = 4 is composite; does this continue? - Charles R Greathouse IV, Nov 25 2014

Links

Table of n, a(n) for n=1..28.

Formula

{n: |A006495(n)| in A000040}.

Maple

A006495 := proc(n) add((-4)^l*binomial(n, 2*l), l=0..floor(n/2)) ; end proc:
isA073019 := proc(n) isprime(abs(A006495(n))) ; end proc:
for n from 1 do if isA073019(n) then print(n) ; end if; end do: # R. J. Mathar, Sep 06 2011

Mathematica

x=1; For[n=1, n<=14000, n++, {x=(1+2*I)*x, If[PrimeQ[Re[x]], Print[n]]}]

Prog

(PARI) is(n)=ispseudoprime(abs(real((1+2*I)^n))) \\ Charles R Greathouse IV, Nov 21 2014

Crossrefs

Cf. A006495.

Sequence in context: A046022 A175787 A345899 * A174291 A007885 A192586

Adjacent sequences: A073016 A073017 A073018 * A073020 A073021 A073022

Keyword

nonn

Author

Benoit Cloitre, Aug 03 2002

Extensions

Edited by John W. Layman, Aug 13 2002

a(21) from Robert G. Wilson v, Aug 22 2002

a(22)-a(28) from Charles R Greathouse IV, Nov 25 2014

Status

approved