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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: A336055 A131925 A128010 * A114740 A330523 A128008 Adjacent sequences: A185043 A185044 A185045 * A185047 A185048 A185049 KEYWORD nonn AUTHOR Michel Lagneau, Apr 17 2013 STATUS approved

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Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)