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

Author

Amarnath Murthy, Aug 15 2002

Keywords

• nonn
• base

Examples

			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.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..1000

Crossrefs

Equals A067180(A002808(n)). Cf. A111397.

Programs

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]];

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).

Extensions

a(19)-a(32) from Stefan Steinerberger, Nov 09 2005

a(33)-a(56) by Robert G. Wilson v, Nov 10 2005