A181495 -id:A181495

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A181492

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

+10
7

7, 13, 193, 786433

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..4.

FORMULA

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

MATHEMATICA

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

PROG

(PARI) for( k=1, 999, ispseudoprime(3<<k-1)|next; ispseudoprime(3<<k+1)|next; print1(3<<k+1, ", "))

CROSSREFS

Cf. A001097, A001359, A006512, A014574.

KEYWORD

nonn

AUTHOR

M. F. Hasler, Oct 30 2010

STATUS

approved

A268515

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

+10
1

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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]

REFERENCES

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

LINKS

Table of n, a(n) for n=1..24.

CROSSREFS

Cf. A002945, A181495 (positions of records).

KEYWORD

nonn,more

AUTHOR

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

EXTENSIONS

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

STATUS

approved

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