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A307368
a(n) is the minimal positive integer such that 2*a(n)*prime(n)-1 equals another prime.
1
1, 1, 2, 1, 2, 4, 2, 1, 3, 3, 1, 1, 2, 3, 3, 2, 3, 4, 3, 2, 7, 1, 2, 8, 1, 5, 3, 3, 3, 3, 3, 2, 2, 1, 5, 6, 1, 3, 5, 2, 5, 4, 11, 4, 2, 1, 1, 4, 2, 1, 8, 3, 7, 6, 6, 2, 3, 1, 6, 2, 3, 2, 1, 5, 3, 3, 1, 1, 3, 4, 5, 3, 1, 3, 1, 2, 3, 3, 11, 4, 8, 6, 2, 4, 1, 3, 3, 3, 6, 3, 2, 5, 6, 5, 1, 2, 9, 2, 3, 4, 1, 5, 2, 3, 4, 1, 2, 2, 3
OFFSET
1,3
COMMENTS
A more general form of Rassias's conjecture states that for every positive integer a there are two primes p and q such that 2*a*p = q+1.
a(n)=1 for n in A137288. - Robert Israel, Apr 18 2019
By Dirichlet's theorem on primes in arithmetic progressions, a(n) exists. - Robert Israel, May 12 2019
REFERENCES
Michael Th. Rassias, Problem-Solving and Selected Topics in Number Theory, Springer-Verlag, NY, 2011, pp. xi-xii.
LINKS
FORMULA
a(n) = A053989(A000040(n))/2 for n <> 3. - Robert Israel, Apr 18 2019
MAPLE
f:= proc(n) local k, p;
p:= ithprime(n);
for k from 1 do
if isprime(2*k*p-1) then return k fi
od
end proc:
map(f, [$1..100]); # Robert Israel, Apr 18 2019
MATHEMATICA
a[n_]:=Module[{a=1}, While[!PrimeQ[2*a*Prime[n]-1], a++]; a];
a/@Range[110]
PROG
(PARI) a(n) = my(p=prime(n)); for(k=1, oo, if(ispseudoprime(2*k*p-1), return(k))) \\ Felix Fröhlich, Apr 17 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ivan N. Ianakiev, Apr 17 2019
STATUS
approved