A265425 Numbers n such that n+2 and sigma(n-1) are both primes.

3, 5, 17, 65, 4097, 65537, 262145, 1073741825

Offset: 1

Author

Jaroslav Krizek, Dec 08 2015

Keywords

• nonn
• more

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

Examples

			Number 17 is in the sequence because 17 + 2 = 19 and sigma(17-1) = sigma(16) = 31; 17 and 31 are primes.
		

Crossrefs

Cf. A000203, A001359, A019434, A023194, A256438.

Programs

Magma

[n: n in [2..1000000] | IsPrime(n+2) and IsPrime(SumOfDivisors(n-1))]

Mathematica

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

PARI

for(n=2, 10^7, if(ispseudoprime(n+2) && ispseudoprime(sigma(n-1)), print1(n, ", "))) \\ Altug Alkan, Dec 08 2015