cp's OEIS Frontend

A117477 Primes whose SOD and that of their indices are both prime and equal (indices may not be prime, but their SOD must be prime).

%I A117477 #13 Apr 21 2024 11:15:19
%S A117477 131,263,1039,1091,1301,1361,1433,2221,2441,2591,2663,2719,2803,3433,
%T A117477 3631,4153,4357,4397,5507,5701,5741,5927,6311,6353,6553,6737,6827,
%U A117477 6971,7013,7213,7411,7523,7741,8821,9103,11173,11353,11731,11821,12277,12347
%N A117477 Primes whose SOD and that of their indices are both prime and equal (indices may not be prime, but their SOD must be prime).
%C A117477 "SOD" = "sum of digits".
%C A117477 This sequence is a subset of A033548, the difference being that this sequence requires prime SODs.
%H A117477 Harvey P. Dale, <a href="/A117477/b117477.txt">Table of n, a(n) for n = 1..1000</a>
%F A117477 Find primes whose indices, when SODs are computed, are both prime and SOD(i) = SOD(p)
%e A117477 a(3) = 1039, the 175th prime. Both the SOD of the index and the prime are prime and equal: 13 = 13.
%t A117477 sodQ[{n_,p_}]:=Module[{sodn=Total[IntegerDigits[n]],sodp=Total[IntegerDigits[p]]},AllTrue[ {sodn,sodp},PrimeQ] && sodn == sodp]; Select[With[{nn=1500},Table[{n,Prime[n]},{n,nn}]],sodQ][[;;,2]] (* _Harvey P. Dale_, Apr 20 2024 *)
%o A117477 (UBASIC)
%o A117477 20 'SOD prime index and SOD prime
%o A117477 30 Y=1
%o A117477 40 Y=nxtprm(Y)
%o A117477 50 C=C+1:print C;Y;"-";
%o A117477 60 D=str(C):Z=str(Y)
%o A117477 70 E=len(D):F=len(Z)
%o A117477 80 for Q=2 to E
%o A117477 90 A=mid(D,Q,1):G=val(A)
%o A117477 100 I=I+G:print I;
%o A117477 110 next Q
%o A117477 120 for R=2 to F
%o A117477 130 B=mid(Z,R,1):H=val(B)
%o A117477 140 J=J+H:print J;
%o A117477 150 next R
%o A117477 160 if I=prmdiv(I) and J=prmdiv(J) and I=J then stop
%o A117477 170 I=0:J=0
%o A117477 180 goto 40
%Y A117477 Cf. A117478, A033548-A033549, A117458-A117463.
%K A117477 easy,nonn,base
%O A117477 1,1
%A A117477 _Enoch Haga_, Mar 19 2006