

A265425


Numbers n such that n+2 and sigma(n1) are both primes.


0




OFFSET

1,1


COMMENTS

If a(9) exists, it must be larger than A023194(10000) = 5896704025969.
Prime terms: 3, 5, 17, 65537, ...
Any prime present must be one of the lesser twin primes (A001359) and also a Fermat prime (A019434), at least. See comments in A023194.  Antti Karttunen, Dec 08 2015
Sequence is different from A256438; numbers 1152921504606846977, 309485009821345068724781057, 81129638414606681695789005144065 and 85070591730234615865843651857942052865 are not terms of this sequence.
Numbers 2^m+1 such that 2^m + 3 and 2^(m+1)  1 are both prime.  Hiroaki Yamanouchi, Jan 04 2016


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

Number 17 is in the sequence because 17 + 2 = 19 and sigma(171) = sigma(16) = 31; 17 and 31 are primes.


MATHEMATICA

Select[Range[10^7], And[PrimeQ[# + 2], PrimeQ[DivisorSigma[1, #  1]]] &] (* Michael De Vlieger, Dec 09 2015 *)


PROG

(MAGMA) [n: n in [2..1000000]  IsPrime(n+2) and IsPrime(SumOfDivisors(n1))]
(PARI) for(n=2, 10^7, if(ispseudoprime(n+2) && ispseudoprime(sigma(n1)), print1(n, ", "))) \\ Altug Alkan, Dec 08 2015


CROSSREFS

Cf. A000203, A001359, A019434, A023194, A256438.
Sequence in context: A085749 A281623 A278741 * A256438 A251737 A125957
Adjacent sequences: A265422 A265423 A265424 * A265426 A265427 A265428


KEYWORD

nonn,more


AUTHOR

Jaroslav Krizek, Dec 08 2015


STATUS

approved



