

A073867


Smallest prime whose digital sum is equal to the nth 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
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..49.


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: A221341 A221106 A271075 * A114782 A065112 A114783
Adjacent sequences: A073864 A073865 A073866 * A073868 A073869 A073870


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



