A181495 -id:A181495 - cp's OEIS frontend

A181492 Primes of the form p=3*2^k+1 such that p-2 is also a prime.

7, 13, 193, 786433

Offset: 1

M. F. Hasler, Oct 30 2010

nonn

Sequence A181490 lists the exponents k, sequences A181491 and A181493 the corresponding lesser twin prime and their average.

a(5) > 3 * 2^3000 + 1. - Max Z. Scialabba, Dec 24 2023

Cf. A001097, A001359, A006512, A014574.

Select[3 2^Range[100]+1,And@@PrimeQ[{#,#-2}]&] (* Harvey P. Dale, Jun 19 2013 *)

PARI
```
for( k=1,999, ispseudoprime(3<
				
```

A181492 = A181491 + 2 = A181493 + 1 = 3*2^A181490 + 1 = intersection of A004119 or A103204 or A181495 with A006512 or A001097.

A268515 Records in A002945 (continued fraction expansion of cube root of 2).

Original entry on oeis.org

1, 3, 5, 8, 14, 15, 534, 7451, 12737, 22466, 68346, 148017, 217441, 320408, 533679, 4156269, 4886972, 10253793, 13761184, 14358891, 35950987, 68665026, 455880544, 10065016098

Offset: 1

N. J. A. Sloane, Feb 07 2016, following a suggestion from Doron Zeilberger

a(1)-a(18) computed by John M. Campbell, Oct 23 2010 (cf. A181495).

It is not known if this sequence is infinite (i.e., whether the continued fraction expansion is bounded). [Davenport]

H. Davenport, The Higher Arithmetic: An Introduction to the Theory of Numbers, Cambridge, 2008.

Cf. A002945, A181495 (positions of records).

a(19)-a(21) from Zak Seidov, Feb 08 2016
a(22)-a(24) from Hans Havermann, Feb 08 2016
Name corrected by Nathan Fox, Feb 08 2016

cp's OEIS Frontend

A181492 Primes of the form p=3*2^k+1 such that p-2 is also a prime.

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