A052022 Smallest number m larger than prime(n) such that prime(n) = sum of digits of m and prime(n) = largest prime factor of m (or 0 if no such number exists).

12, 50, 70, 308, 364, 476, 1729, 4784, 9947, 8959, 38998, 588965, 179998, 1879859, 5988788, 38778989, 79693999, 287978998, 1489989599, 4595969989, 6888999949, 45999897788, 197999598599, 3999966997975, 6849998899886, 7885998969988, 35889999789995, 39969896999968

Offset: 2

Author

Patrick De Geest, Nov 15 1999

Keywords

• nonn
• base
• nice

Comments

Does there exist a solution for every prime p?

Examples

			p=43 -> a(14)=179998 -> 1+7+9+9+9+8 = 43 and 179998 = 2*7*13*23*43. p=47 -> a(15)=1879859 -> 1+8+7+9+8+5+9 = 47 and 1879859 = 23*37*47*47.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..34

Crossrefs

Cf. A052018, A052019, A052020, A052021, A007953, A005349, A028834.

Programs

Maple

A052022(n) = {
  local( p,m );
  p=prime(n) ;
  for(k=2,1000000000,
    m=k*p;
    if( A007953(m) == p && A006530(m) == p,
        return(m) ;
    )
  ) ;
} # R. J. Mathar, Mar 02 2012

Mathematica

snm[n_]:=Module[{k=2,p=Prime[n],m},m=k p;While[Total[ IntegerDigits[ m]]!=p||FactorInteger[m][[-1,1]]!=p,k++;m=k p];m]; Array[snm,18,2] (* Harvey P. Dale, Feb 28 2012 *)

PARI

a(n) = my(p=prime(n), k=2, m=k*p); while ((sumdigits(m) != p) || (vecmax(factor(m)[,1]) != p), k++; m = k*p); m; \\ Michel Marcus, Apr 09 2021

Extensions

a(20)-a(29) from Donovan Johnson, May 09 2012