A054750 Smallest prime number whose digits sum to n-th prime.

2, 3, 5, 7, 29, 67, 89, 199, 599, 2999, 4999, 29989, 59999, 79999, 389999, 989999, 6999899, 8989999, 59899999, 89999999, 289999999, 799999999, 3999998999, 19999997999, 79999999999, 399999998999, 599999899999, 999998999999

Offset: 1

Author

G. L. Honaker, Jr., Apr 24 2000

Keywords

• base
• nonn

Comments

a(n) >= A051885(A000040(n)). Indices n for which the equality holds are listed in A055019.

a(n) >= A046864(n). - Michel Marcus, Nov 01 2015

Examples

			a(7)=89 because 8+9=17 and 17 is the 7th prime.
		

Links

• Chris Caldwell and G. L. Honaker, Jr., Prime curio for 8999

Crossrefs

Cf. A000040, A067180, A046704, A046864, A068951, A007605.

Programs

Mathematica

a[n_]:=Module[{k=2}, While[DigitSum[k]!=Prime[n], k=NextPrime[k]]; k]; Array[a,15] (* Stefano Spezia, Mar 27 2025 *)

PARI

a(n) = {my(k=2); my(p=prime(n)); while((sumdigits(k) != prime(n)), k=nextprime(k+1)); k;} \\ Michel Marcus, Nov 01 2015

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 31 2000

Edited and extended by Robert G. Wilson v, Feb 26 2002