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A103514
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a(n) = smallest m such that primorial(n)/2 - 2^m is prime.
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24
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0, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 25, 2, 1, 6, 6, 19, 1, 13, 3, 3, 11, 29, 2, 1, 6, 3, 4, 2, 6, 4, 15, 6, 4, 20, 4, 1, 7, 16, 4, 7, 22, 3, 12, 13, 9, 35, 2, 3, 3, 52, 35, 3, 32, 15, 13, 10, 53, 56, 9, 16, 36, 5, 8, 5, 22, 3, 14, 2, 64, 37, 8, 22, 42, 11, 22, 22, 12, 11, 26, 1, 54, 187, 20, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,9
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COMMENTS
| Values of n in A103153. Conjecture: sequence is defined for all k>=2.
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EXAMPLE
| P(2)/2-2^0=2 is prime, so a(2)=0;
P(10)/2-2^3=3234846607 is Prime, so a(10)=3.
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MATHEMATICA
| nmax = 2^8192; npd = 1; n = 2; npd = npd*Prime[n]; While[npd < nmax, tn = 1; tt = 2; cp = npd - tt; While[(cp > 1) && (! (PrimeQ[cp])), tn = tn + 1; tt = tt*2; cp = npd - tt]; If[cp < 2, Print["*"], Print[tn]]; n = n + 1; npd = npd*Prime[n]]
k = 1; a = {}; Do[k = k*Prime[n]; m = 1; While[ ! PrimeQ[k - 2^m], m++ ]; Print[m]; AppendTo[a, m], {n, 2, 200}]; a (*Artur Jasinski, Apr 21 2008 *)
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CROSSREFS
| Cf. A002110, A005234, A014545, A018239, A006794, A057704, A057705, A103153.
Cf. A067026, A067027, A139439, A139440, A139441, A139442, A139443, A139444, A139445, A139446, A139447, A139448, A139449, A139450, A139451, A139452, A139453, A139454, A139455, A139456, A139457, A103514.
Sequence in context: A078897 A011086 A188584 * A016570 A070773 A046804
Adjacent sequences: A103511 A103512 A103513 * A103515 A103516 A103517
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KEYWORD
| nonn
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AUTHOR
| Lei Zhou (lzhou5(AT)emory.edu), Feb 15 2005
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), May 16 2008 at the suggestion of R. J. Mathar
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