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A282342 a(n) is the smallest prime number, with sum of digits equals n and a(n) is greater than previous nonzero terms, except if this is not possible in which case a(n)=0.

%I A282342 #41 Jun 02 2025 12:20:41
%S A282342 0,2,3,13,23,0,43,53,0,73,83,0,139,149,0,277,359,0,379,389,0,499,599,
%T A282342 0,997,1889,0,1999,2999,0,4999,6899,0,17989,18899,0,29989,39989,0,
%U A282342 49999,59999,0,79999,98999,0,199999,389999,0,598999,599999,0,799999,989999,0,2998999
%N A282342 a(n) is the smallest prime number, with sum of digits equals n and a(n) is greater than previous nonzero terms, except if this is not possible in which case a(n)=0.
%C A282342 I conjecture that there are prime numbers for every n, if n is not divisible by 3.
%C A282342 Other terms:
%C A282342 a(97) = 79999999999;
%C A282342 a(98) = 98999999999;
%C A282342 a(100) = 298999999999;
%C A282342 a(1000) = 299989999999999999999999999999999999999999999999999999999999999999
%C A282342           9999999999999999999999999999999999999999999999.
%e A282342 a(23) = 599 because 599 is a prime number greater than a(22) = 499 and the sum of its digits is 5 + 9 + 9 = 23.
%e A282342 a(24) = 0 because 24 (mod 3) = 0.
%t A282342 a = {1}; Do[If[n != 3 && Divisible[n, 3], AppendTo[a, 0], p = NextPrime@ Max@ a; While[Total@ IntegerDigits@ p != n, p = NextPrime@ p]; AppendTo[a, p]], {n, 2, 57}]; a (* _Michael De Vlieger_, Feb 12 2017 *)
%o A282342 (PARI) {
%o A282342 print1(0", "2", ");
%o A282342 n=3;p=3;sp=3;
%o A282342 while(p<1000000,
%o A282342         while(sp<>n,
%o A282342                   p=nextprime(p+1);
%o A282342                   sp=sumdigits(p);
%o A282342                 );
%o A282342                  print1(p", ");
%o A282342                  n++;if(n%3==0,n++;print1(0", "));
%o A282342         )
%o A282342 }
%Y A282342 Cf. A067180.
%K A282342 nonn,base
%O A282342 1,2
%A A282342 _Dimitris Valianatos_, Feb 12 2017