A073867 Smallest prime whose digital sum is equal to the n-th composite number, or 0 if no such prime exists.

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

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: A221106 A271075 A345191 * 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