A117458 Primes and their indices such that when their respective SOD's are both prime, the SOD of the index is the nextprime of the prime SOD.
227, 313, 1723, 2003, 2311, 2609, 3329, 3701, 4007, 4027, 4801, 4931, 5107, 7253, 10457, 12143, 12163, 12211, 12433, 12547, 13063, 14143, 14341, 14831, 15139, 15373, 16091, 17027, 17047, 19403, 20047, 20261, 21059, 21149, 22157, 23053, 23293, 23431, 24229, 24623
Offset: 1
Examples
313 is a term, 65 is the index of the prime 313. The SOD(65) = 11. The SOD(313) = 7. 11 is the next prime after 7.
Programs
-
Mathematica
Select[Range[25000], PrimeQ[#] && PrimeQ[Plus @@ IntegerDigits[#]] && NextPrime[Plus @@ IntegerDigits[#]] == Plus @@ IntegerDigits[PrimePi[#]] &] (* Tanya Khovanova, Mar 16 2021 *)
Formula
Individually sum the digits of both prime index and associated prime. If both sums are prime and the sum of the index is the next prime of the prime SOD, add to sequence.
Extensions
Offset changed to 1 by Alois P. Heinz, Mar 16 2021
Comments