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

2,1

Comments

Does there exist a solution for every prime p?

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A029586 A335698 A081292 * A110907 A009937 A009932

Adjacent sequences: A052019 A052020 A052021 * A052023 A052024 A052025

Keyword

nonn,base,nice

Author

Patrick De Geest, Nov 15 1999

Extensions

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

Status

approved