%I #31 Apr 09 2021 10:42:39

%S 12,50,70,308,364,476,1729,4784,9947,8959,38998,588965,179998,1879859,

%T 5988788,38778989,79693999,287978998,1489989599,4595969989,6888999949,

%U 45999897788,197999598599,3999966997975,6849998899886,7885998969988,35889999789995,39969896999968

%N 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).

%C Does there exist a solution for every prime p?

%H Chai Wah Wu, <a href="/A052022/b052022.txt">Table of n, a(n) for n = 2..34</a>

%e 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.

%p A052022(n) = {

%p local( p,m );

%p p=prime(n) ;

%p for(k=2,1000000000,

%p m=k*p;

%p if( A007953(m) == p && A006530(m) == p,

%p return(m) ;

%p )

%p ) ;

%p } # _R. J. Mathar_, Mar 02 2012

%t 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 *)

%o (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

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

%K nonn,base,nice

%O 2,1

%A _Patrick De Geest_, Nov 15 1999

%E a(20)-a(29) from _Donovan Johnson_, May 09 2012