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Search: id:A073867
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| A073867 |
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Smallest prime whose digital sum is equal to the n-th composite number, or 0 if no such prime exists. |
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+0
4
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| 13, 0, 17, 0, 19, 0, 59, 0, 79, 0, 389, 0, 499, 0, 997, 1889, 0, 1999, 0, 6899, 0, 17989, 8999, 0, 39989, 0, 49999, 0, 98999, 0, 199999, 0, 598999, 599999, 0, 799999, 0, 2998999, 2999999, 0, 4999999, 0, 9899999, 0, 19999999, 29999999, 0, 59999999, 0
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n)=0 iff that composite number (A002808(n)) is congruent to 0 (modulo 3), otherwise a(n)=A007605(k) for the first k that equals A002808(n).
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EXAMPLE
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The first composite number (A002808) is 4 and the least prime whose digital sum is 4 is 13.
The second composite number (A002808) is 6 whose digital sum is == 0 (mod 3) so there is no prime whose fits the definition.
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MATHEMATICA
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Composite[n_] := FixedPoint[n + PrimePi[ # ] + 1 &, n]; f[n_] := Block[{cn = Composite[n]}, k = 1; While[Plus @@ IntegerDigits@Prime@k != cn, k++ ]; Prime[k]];
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CROSSREFS
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Equals A067180(A002808(n)). Cf. A111397.
Sequence in context: A127708 A094896 A067155 this_sequence A114782 A065112 A114783
Adjacent sequences: A073864 A073865 A073866 this_sequence A073868 A073869 A073870
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KEYWORD
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nonn,base
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 15 2002
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EXTENSIONS
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a(19)-a(32) from Stefan Steinerberger (hansibal(AT)hotmail.com), Nov 09 2005
a(33)-a(56) by Robert G. Wilson v (rgwv(at)rgwv.com), Nov 10 2005
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