

A073019


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


0



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
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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: A211781 A046022 A175787 * 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



