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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A000040, A053989, A137288.

Sequence in context: A164281 A082693 A225081 * A097082 A281729 A302290

Adjacent sequences:  A307365 A307366 A307367 * A307369 A307370 A307371

KEYWORD

nonn

AUTHOR

Ivan N. Ianakiev, Apr 17 2019

STATUS

approved

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Last modified August 2 02:30 EDT 2021. Contains 346409 sequences. (Running on oeis4.)