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A236248
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Numbers m with C(2*m, m) - prime(m) prime, where C(2*m, m) = (2*m)!/(m!)^2.
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5
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2, 5, 6, 10, 29, 132, 266, 322, 350, 538, 667, 693, 776, 977, 1336, 1810, 1908, 1980, 2175, 2616, 2716, 3211, 3473, 5223, 5630, 5758, 6585, 6979, 7964, 8469, 9052, 9758, 10324, 16876, 25760, 28171
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OFFSET
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1,1
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COMMENTS
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According to the conjecture in A236256, this sequence should have infinitely many terms.
The prime C(2*a(36), a(36)) - prime(a(36)) = C(56342, 28171) - prime(28171) has 16959 decimal digits.
See A236249 for primes of the form C(2*m, m) - prime(m).
See also A236242 for a similar sequence.
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LINKS
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EXAMPLE
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a(1) = 2 since C(2*1, 1) - prime(1) = 2 - 2 = 0 is not prime, but C(2*2, 2) - prime(2) = 6 - 3 = 3 is prime.
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MATHEMATICA
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n=0; Do[If[PrimeQ[Binomial[2m, m]-Prime[m]], n=n+1; Print[n, " ", m]], {m, 1, 10000}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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