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A185046 Smallest prime p such that 2n+1 = p^3 - 2q for some odd prime q, or 0 if no such prime exists. 4
5, 3, 5, 7, 13, 3, 13, 3, 5, 3, 3, 11, 0, 7, 5, 19, 37, 11, 5, 7, 5, 7, 37, 11, 5, 31, 53, 31, 13, 23, 5, 7, 5, 7, 13, 23, 13, 19, 5, 7, 421, 47, 5, 7, 5, 11, 13, 11, 5, 43, 5, 11, 61, 23, 5, 19, 5, 7, 5, 5, 53, 7, 17, 7, 13, 11, 13, 7, 113, 7, 373, 11, 17, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = 0 for n = 13, 171, 364, 1098, 2456, 3429, 6083, 7812, 9841, 12194, 14895, 17968,... and 2n+1 = 27, 343, 729,... is a class of cubes.

The corresponding primes q are in A224730.

Conjecture: The odd numbers different from a cube are of the form m = p^3 - 2q where p and q are prime numbers.

Remark: Its converse is false: there exists cubes m = c^3 that are in the sequence with the form c^3 = p^3 - 2q, where p-c = 2, and q of the form x^2 +x*y+y^2 (see A007645). For example: 5^3 = 7^3 - 2*109.

LINKS

Michel Lagneau, Table of n, a(n) for n = 1..10000

EXAMPLE

a(4) = 7 because, for (p, q) = (7, 167) => 2*4+1 = 9 = 7^3 - 2*167 = 343 - 334 = 9.

MAPLE

for n from 3 by 2 to 200 do:

      jj:=0:

          for j from 1 to 10000 while (jj=0) do:

             p:=ithprime(j):q:=(p^3-n)/2:

             if q> 0 and type(q, prime)=true

             then

             jj:=1:printf(`%d, `, p):

             else

             fi:

         od:

            if jj=0 then

            printf(`%d, `, 0):

            else

            fi:

     od:

CROSSREFS

Cf. A007645, A224730.

Sequence in context: A269893 A131925 A128010 * A114740 A128008 A265800

Adjacent sequences:  A185043 A185044 A185045 * A185047 A185048 A185049

KEYWORD

nonn

AUTHOR

Michel Lagneau, Apr 17 2013

STATUS

approved

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Last modified May 19 08:25 EDT 2019. Contains 323389 sequences. (Running on oeis4.)