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A224730 Smallest prime q such that 2n+1 = p^3 - 2q for some odd prime p, or 0 if no such prime exists. 4

%I

%S 61,11,59,167,1093,7,1091,5,53,3,2,653,0,157,47,3413,25309,647,43,151,

%T 41,149,25303,641,37,14869,74411,14867,1069,6053,31,139,29,137,1063,

%U 6047,1061,3391,23,131,37309189,51869,19,127,17,619,1051,617,13,39703,11

%N Smallest prime q such that 2n+1 = p^3 - 2q for some odd prime p, or 0 if no such prime exists.

%C See the conjecture and the comments in A185046, and the corresponding primes p.

%H Michel Lagneau, <a href="/A224730/b224730.txt">Table of n, a(n) for n = 1..10000</a>

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

%p for n from 3 by 2 to 200 do:

%p jj:=0:

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

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

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

%p then

%p jj:=1:printf(`%d, `, q):

%p else

%p fi:

%p od:

%p if jj=0 then

%p printf(`%d, `, 0):

%p else

%p fi:

%p od:

%Y Cf. A185046.

%K nonn

%O 1,1

%A _Michel Lagneau_, Apr 17 2013

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Last modified January 28 14:40 EST 2023. Contains 359895 sequences. (Running on oeis4.)