%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