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A222227 Numbers n such that n and n + 16 are prime and there is a power of two in the interval (n,n+16). 2
3, 7, 13, 31, 241, 65521, 1048573, 2305843009213693951 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is a conjecture that this is a finite sequence. A search was conducted out to 2^1500.

LINKS

Table of n, a(n) for n=1..8.

PROG

(MAGMA)

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

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

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

//checked by inspection.

gap:=16;

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;

CROSSREFS

Cf. A049488, A221211.

Sequence in context: A023195 A100382 A292448 * A152981 A112040 A222187

Adjacent sequences:  A222224 A222225 A222226 * A222228 A222229 A222230

KEYWORD

nonn

AUTHOR

Brad Clardy, Feb 23 2013

STATUS

approved

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Last modified November 21 12:11 EST 2019. Contains 329370 sequences. (Running on oeis4.)