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

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A272061 Primes p such that sigma((p-1)/2) + tau((p-1)/2) is prime. 2
3, 5, 17, 257, 65537, 453519617, 1372257937, 1927561217, 21320672257, 76001667857 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p such that A000203((p-1)/2) + A000005((p-1)/2) is a prime q.

Corresponding values of primes q: 2, 5, 19, 263, 65551, 496922891, ...

Prime terms from A272060.

The first 5 known Fermat primes from A019434 are in this sequence.

Primes of the form 2*m+1 with m a term of A064205. - Michel Marcus, Apr 25 2016

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

sigma((17-1)/2) + tau((17-1)/2) = sigma(8) + tau(8) = 15 + 4 = 19; 19 is prime, so 17 is in the sequence.

MAPLE

with(numtheory): A272061:=n->`if`(isprime(n) and isprime(sigma((n-1)/2)+tau((n-1)/2)), n, NULL): seq(A272061(n), n=3..10^5); # Wesley Ivan Hurt, Apr 20 2016

MATHEMATICA

Select[Prime[Range[10000]], PrimeQ[DivisorSigma[1, (#-1)/2] + DivisorSigma[0, (#-1)/2]] & ] (* Robert Price, Apr 21 2016 *)

PROG

(MAGMA) [n: n in [3..1000000] | IsPrime(n) and IsPrime(NumberOfDivisors((n-1) div 2) + SumOfDivisors((n-1) div 2)) and (n-1) mod 2 eq 0]

(PARI) isok(n) = isprime(sigma((n-1)/2) + numdiv((n-1)/2));

lista(nn) = forprime (p=3, nn, if (isok(p), print1(p, ", "))); \\ Michel Marcus, Apr 19 2016

(PARI) is(n)=my(f=factor(n\2)); isprime(sigma(f)+numdiv(f)) && isprime(n) \\ Charles R Greathouse IV, Apr 28 2016

CROSSREFS

Cf. A000005, A000203, A055813, A064205, A272060.

Sequence in context: A070592 A254576 A232720 * A247203 A262534 A000215

Adjacent sequences:  A272058 A272059 A272060 * A272062 A272063 A272064

KEYWORD

nonn,more

AUTHOR

Jaroslav Krizek, Apr 19 2016

EXTENSIONS

a(7)-a(8) from Michel Marcus, Apr 24 2016

a(9) from Charles R Greathouse IV, Apr 29 2016

a(10) from Charles R Greathouse IV, Apr 29 2016

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 28 21:38 EDT 2017. Contains 287241 sequences.