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A221211 Numbers n such that n and n + 4 are prime and there is a power of two in the interval (n,n+4). 7
3, 7, 13, 127 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is a conjecture that this is a finite sequence. These may be the only known cousin primes with this property.

The Cf.s list similar sequences, of the form -- numbers n such that n and n+m are prime and contain a power of two in the interval (n,n+m). The case where m=2, the twin prime case -- not listed, has only one member n=3. Another member would have to be a twin where n+2 was a Fermat type prime and n a Mersenne prime.

LINKS

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

PROG

(MAGMA)

//Program finds primes separated by an even number (called gap) which

//have a power of two between them. The program starts with the smallest

//of two above gap. Primes less than this starting point can be checked by

//inspection. In this example 3 also works.

gap:=4;

start:=Ilog2(gap)+1;

for i:= start to 1000 do

    powerof2:=2^i;

    for k:=powerof2-gap+1 to powerof2-1 by 2 do

        if (IsPrime(k) and IsPrime(k+gap)) then k;

        end if;

    end for;

end for;

(MAGMA) [n: n in PrimesUpTo(10^3) | IsPrime(n+4) and exists{t: t in [n+1..n+3 by 2] | IsOne(t/2^Valuation(t, 2))}]; // Bruno Berselli, May 16 2013

CROSSREFS

Cf. A023200.

Cf. A220951 (gap of 6), A213210 (8), A220746 (10), A213677 (12), A222424 (14), A222227 (16), A222219 (18).

Sequence in context: A038691 A237890 A082718 * A322301 A154821 A084741

Adjacent sequences:  A221208 A221209 A221210 * A221212 A221213 A221214

KEYWORD

nonn

AUTHOR

Brad Clardy, Feb 21 2013

STATUS

approved

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Last modified January 22 00:08 EST 2022. Contains 350481 sequences. (Running on oeis4.)