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Search: id:A105418
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| A105418 |
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Smallest prime p such that the sum of it and the following prime have n prime factors including multiplicity, or 0 if no such prime exists. |
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+0
1
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| 2, 0, 3, 11, 53, 71, 61, 191, 953, 1151, 3833, 7159, 4093, 30713, 36857, 110587, 360439, 663547, 2064379, 786431, 3932153, 5242877, 9437179, 63700991, 138412031, 169869311, 436207613, 3875536883, 1358954453, 1879048183
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(2) = 0 since it is impossible.
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EXAMPLE
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a(5) = 53 because (53 + 59) = 112 = 2^4*7.
a(24) = 63700991 because (63700991 + 63700993) = 127401984 = 2^19*3^5.
a(28) = 3875536883 because (3875536883 + 3875536909) = 7751073792 = 2^25*3*7*11.
a(29) = 1358954453 because (1358954453 + 1358954539) = 2717908992 = 2^25*3^4.
a(30) = 1879048183 because (1879048183 + 1879048201) = 3758096384 = 2^29*7.
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MATHEMATICA
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f[n_] := Plus @@ Flatten[ Table[ #[[2]], {1}] & /@ FactorInteger[n]]; t = Table[0, {40}]; Do[a = f[Prime[n] + Prime[n + 1]]; If[a < 41 && t[[a]] == 0, t[[a]] = Prime[n]; Print[{a, Prime[n]}]], {n, 111500000}]; t
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CROSSREFS
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Cf. A071215.
Sequence in context: A071411 A121065 A077928 this_sequence A135433 A104774 A087263
Adjacent sequences: A105415 A105416 A105417 this_sequence A105419 A105420 A105421
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KEYWORD
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nonn
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it) and Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 06 2005
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EXTENSIONS
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a(28)=3875536883 from Ray Chandler (rayjchandler(AT)sbcglobal.net) and Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 10 2005
Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Apr 10 2005
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