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).
131, 263, 1039, 1091, 1301, 1361, 1433, 2221, 2441, 2591, 2663, 2719, 2803, 3433, 3631, 4153, 4357, 4397, 5507, 5701, 5741, 5927, 6311, 6353, 6553, 6737, 6827, 6971, 7013, 7213, 7411, 7523, 7741, 8821, 9103, 11173, 11353, 11731, 11821, 12277, 12347
Offset: 1
Examples
a(3) = 1039, the 175th prime. Both the SOD of the index and the prime are prime and equal: 13 = 13.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
-
Mathematica
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 *) -
UBASIC
20 'SOD prime index and SOD prime 30 Y=1 40 Y=nxtprm(Y) 50 C=C+1:print C;Y;"-"; 60 D=str(C):Z=str(Y) 70 E=len(D):F=len(Z) 80 for Q=2 to E 90 A=mid(D,Q,1):G=val(A) 100 I=I+G:print I; 110 next Q 120 for R=2 to F 130 B=mid(Z,R,1):H=val(B) 140 J=J+H:print J; 150 next R 160 if I=prmdiv(I) and J=prmdiv(J) and I=J then stop 170 I=0:J=0 180 goto 40
Formula
Find primes whose indices, when SODs are computed, are both prime and SOD(i) = SOD(p)
Comments