login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112633 Mersenne prime indices that are also Gaussian primes. 10
3, 7, 19, 31, 107, 127, 607, 1279, 2203, 4423, 86243, 110503, 216091, 756839, 1257787, 20996011, 24036583, 25964951, 37156667 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also, primes p (A000043) such that 2^p-1 is prime (A000668) and congruent to 7 mod 5!. - Artur Jasinski, Sep 30 2008. Proof that this is the same sequence, from Jeppe Stig Nielsen, Jan 02 2018: An odd index p>2 will be either 1 or 3 mod 4. If it is 1, then 2^p = 2^(4k+1) will be 2 mod 5, and be 0 mod 4, and be 2 mod 3. This completely determines 2^p (and hence 2^p - 1) mod 5!. The other case, when p is 3 mod 4, will make 2^p congruent to 3 mod 5, to 0 mod 4, and to 2 mod 3. This leads to the other (distinct) value of 2^p mod 5!.

LINKS

Table of n, a(n) for n=1..19.

FORMULA

The intersection of A000043 and A002145. - R. J. Mathar, Oct 06 2008

MATHEMATICA

p = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 43112609}; a = {}; Do[If[Mod[2^p[[n]] - 1, 5! ] == 7, AppendTo[a, p[[n]]]], {n, 1, Length[p]}]; a (* Artur Jasinski, Sep 30 2008 *)

Select[{2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 43112609}, Mod[2^#-1, 120]==7&] (* Harvey P. Dale, Nov 26 2013 *)

CROSSREFS

Cf. A112634, A112648, A112649.

Cf. also A000043, A000668, A124477, A139484, A145039, A145040, A145041, A145042.

Sequence in context: A077313 A102271 A145039 * A113916 A227502 A268065

Adjacent sequences:  A112630 A112631 A112632 * A112634 A112635 A112636

KEYWORD

nonn,more

AUTHOR

Jorge Coveiro, Dec 27 2005

EXTENSIONS

Edited by N. J. A. Sloane, Jan 06 2018

a(19) from Ivan Panchenko, Apr 12 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 22:12 EDT 2019. Contains 322328 sequences. (Running on oeis4.)