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A073867
Smallest prime whose digital sum is equal to the n-th composite number, or 0 if no such prime exists.
4
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
OFFSET
1,1
FORMULA
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).
EXAMPLE
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.
MATHEMATICA
Composite[n_] := FixedPoint[n + PrimePi[ # ] + 1 &, n]; f[n_] := Block[{cn = Composite[n]}, k = 1; While[Plus @@ IntegerDigits@Prime@k != cn, k++ ]; Prime[k]];
CROSSREFS
Equals A067180(A002808(n)). Cf. A111397.
Sequence in context: A221106 A271075 A345191 * A114782 A065112 A114783
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, Aug 15 2002
EXTENSIONS
a(19)-a(32) from Stefan Steinerberger, Nov 09 2005
a(33)-a(56) by Robert G. Wilson v, Nov 10 2005
STATUS
approved