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A063897 a(n) is the least k such that k - A000215(j), j=0..n, are all primes. 1
5, 8, 22, 274, 65704, 4295145556, 18446744073810262144 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Is this sequence finite?

The prime k-tuples conjecture implies that the sequence is infinite. - Robert Israel, Jul 11 2016

LINKS

Table of n, a(n) for n=0..6.

EXAMPLE

For j=0 a(0)=5 because 5-3 is prime.

For j=1 a(1)=8 because 8-5, 8-3 are all primes.

For j=2 a(2)=22 because 22-17, 22-5, 22-3 are all primes.

For j=3 a(3)=274 because 274-257, 274-17, 274-5, 274-3 are all primes.

MAPLE

f:= proc(n) local r, j, good;

for r from 2^(2^n)+4 by 2 do

good:= true;

for j from 0 to n do

if not isprime(r - 2^(2^j)-1) then good:= false; break fi

od;

if good then return(r) fi

od

end proc:

f(0):= 5:

map(f, [$0..5]); # Robert Israel, Jul 11 2016

PROG

(PARI) okprime(mink, vecf) = {for (i = 1, #vecf, if (! isprime(mink - vecf[i]), return (0)); ); return (1); }

a(n) = {mink = 2^(2^n) + 2; vecf = vector(n+1, i, 2^(2^(i-1)) + 1); while (! okprime(mink, vecf), mink++); mink; } \\ Michel Marcus, Sep 28 2013

CROSSREFS

Cf. A000215.

Sequence in context: A120041 A120042 A120043 * A092733 A116884 A192651

Adjacent sequences: A063894 A063895 A063896 * A063898 A063899 A063900

KEYWORD

hard,more,nonn

AUTHOR

Felice Russo, Aug 29 2001

EXTENSIONS

18446744073810262144 from Thomas Baruchel, Oct 21 2003

STATUS

approved

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Last modified December 10 02:09 EST 2022. Contains 358712 sequences. (Running on oeis4.)