A217376 Numbers n such that n, 2n-1 and 2n+1 all are prime or a prime power.

2, 3, 4, 5, 9, 13, 41, 121

Offset

1,1

Comments

a(9) = (3^541-1)/2. - Conjectured by Jack Brennen, Oct 01 2012; confirmed by Max Alekseyev, Nov 10 2019

Since one of n, 2n-1, 2n+1 is divisible by 3 and thus is a power of 3, every term has one of the forms: 3^k, (3^k-1)/2, or (3^k+1)/2. - Max Alekseyev, Nov 10 2019

Links

Max Alekseyev, Table of n, a(n) for n = 1..9

W. Smith and others, n, 2n-1, 2n+1 all prime or prime-power (maybe n-2 also), on primenumbers Yahoo! group, Oct 01 2012.

Warren Smith, Jack Brennen, Phil Carmody, n, 2n-1, 2n+1 all prime or prime-power (maybe n-2 also), digest of 6 messages in primenumbers Yahoo group, Oct 1, 2012.

Mathematica

Select[Range[200], Length[FactorInteger[#]]==Length[FactorInteger[2#-1]] == Length[FactorInteger[2#+1]]==1&] (* Harvey P. Dale, Oct 12 2012 *)

Prog

(PARI) for(n=1, 9e9, omega(n)==1 & omega(2*n-1)==1 & omega(2*n+1)==1 & print1(n", ")) \\ - M. F. Hasler, Oct 01 2012
(Magma) [k:k in [2..1000]| forall{s:s in [k, 2*k-1, 2*k+1]| #PrimeDivisors(s) eq 1}]; // Marius A. Burtea, Nov 13 2019

Crossrefs

Sequence in context: A245449 A337647 A346600 * A050160 A230769 A099472

Adjacent sequences: A217373 A217374 A217375 * A217377 A217378 A217379

Keyword

nonn

Author

M. F. Hasler, after an idea from Warren Smith, Oct 01 2012

Status

approved