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A078097
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Least m such that P - m is prime, where P is the n-th perfect number.
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1
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1, 5, 5, 5, 5, 17, 9, 65, 93, 129, 627, 111, 407, 795, 377, 1509, 257, 5207, 1233, 8537, 3917, 20253, 4613, 15435, 5619, 43823
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OFFSET
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1,2
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COMMENTS
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Some of the larger entries may only correspond to probable primes.
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LINKS
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MATHEMATICA
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e (* from A000043 *) = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, ...}; PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; Do[p = 2^(e[[n]] - 1)*(2^e[[n]] - 1); Print[p - PrevPrim[p]], {n, 1, 20}]
#-NextPrime[#, -1]&/@PerfectNumber[Range[15]] (* The program generates the first 15 terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Nov 22 2023 *)
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CROSSREFS
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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