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

1,1

Comments

"SOD" = "sum of digits".

Links

Table of n, a(n) for n=1..40.

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.

Example

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.

Mathematica

Select[Range[25000],  PrimeQ[#] && PrimeQ[Plus @@ IntegerDigits[#]] &&
   NextPrime[Plus @@ IntegerDigits[#]] == Plus @@ IntegerDigits[PrimePi[#]] &] (* Tanya Khovanova, Mar 16 2021 *)

Crossrefs

Cf. A000720, A007953, A117459, A117460, A117461, A117462, A117463.

Sequence in context: A259059 A333425 A142261 * A252026 A210513 A142842

Adjacent sequences: A117455 A117456 A117457 * A117459 A117460 A117461

Keyword

easy,nonn,base

Author

Enoch Haga, Mar 18 2006

Extensions

Offset changed to 1 by Alois P. Heinz, Mar 16 2021

Status

approved