cp's OEIS Frontend

A117461 Indices associated with primes in A117460. Both primes and their indices, after calculation of their respective digit sums, bear the relationship that both are prime and that sod(i) < sod(p) and sod(p) is the next prime after to sod(i), where sod is the sum of digits function.

%I A117461 #17 Apr 21 2024 11:39:14
%S A117461 1,2,3,14,30,43,74,142,184,214,238,241,256,287,292,308,313,346,443,
%T A117461 449,472,544,593,601,607,623,715,737,791,814,836,854,874,881,883,913,
%U A117461 931,973,980,995,1088,1156,1237,1307,1316,1343,1381,1396,1462,1565,1622
%N A117461 Indices associated with primes in A117460. Both primes and their indices, after calculation of their respective digit sums, bear the relationship that both are prime and that sod(i) < sod(p) and sod(p) is the next prime after to sod(i), where sod is the sum of digits function.
%C A117461 A117458-A117459 is the opposite case where sod(i) > sod(p).
%C A117461 A117460-A117461 is sod(i) < sod(p).
%C A117461 A033548-A033549 is sod(i) = sod(p). - _G. L. Honaker, Jr._
%F A117461 SOD's are calculated for these indices; if they and their associated prime SOD's are both prime and bear the relation in the Brief description above, they are added to the sequence.
%e A117461 a(4) = 30. Its associated prime is 113 with sod = 5; sod(a(4)) = 3. Since 3 < 5 and 5 is the next prime after 3, a(4) belongs in the sequence.
%o A117461 (UBASIC)
%o A117461 10 'use of str,mid,len,val
%o A117461 20 'in SOD prime index and SOD prime
%o A117461 30 Y=1
%o A117461 40 Y=nxtprm(Y)
%o A117461 50 C=C+1:print C;Y;"-";
%o A117461 60 D=str(C):Z=str(Y)
%o A117461 70 E=len(D):F=len(Z)
%o A117461 80 for Q=2 to E
%o A117461 90 A=mid(D,Q,1):G=val(A)
%o A117461 100 I=I+G:print I;
%o A117461 110 next Q
%o A117461 120 for R=2 to F
%o A117461 130 B=mid(Z,R,1):H=val(B)
%o A117461 140 J=J+H:print J;
%o A117461 150 next R
%o A117461 160 if I=prmdiv(I) and J=prmdiv(J) and I<J and J=nxtprm(I) then stop
%o A117461 170 I=0:J=0
%o A117461 180 goto 40
%Y A117461 Cf. A007953 (sum of digits).
%Y A117461 Cf. A117460, A117458, A117459, A033548, A033549.
%K A117461 easy,nonn,base
%O A117461 0,2
%A A117461 _Enoch Haga_, Mar 18 2006