A331031 The prime numbers that are prime-indexed primes and whose digit sum, adjacent digit sum concatenation, and adjacent digit difference concatenation are also primes.

41, 83, 401, 2063, 6863, 10909, 20063, 26489, 44621, 105229, 187067, 205507, 233267, 238547, 240047, 243301, 256307, 346763, 367021, 376003, 395581, 555707, 562181, 563467, 600203, 613243, 644843, 675263, 689789, 785801, 787601, 837667, 845381, 954263, 959389, 1070203

Offset: 1

Author

Scott R. Shannon, Jan 07 2020

Keywords

• nonn
• base

Comments

This sequence lists the prime numbers that are prime-indexed primes, see A006450, and whose digit sum A007953, concatenation of adjacent digit sums A053392, and concatenation of adjacent digit differences A040115, are also primes. This is a subsequence of A006450 and A330653. There are 267 terms for primes up to 20491057.

Examples

			a(4) = 2063 as 2063 is the 311th prime, 2+0+6+3 = 11, '2+0'+'0+6'+'6+3' = 269, '|2-0|'+'|0-6|'+'|6-3|' = 263, and 2063, 311, 11, 269, 263 are all prime.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Wikipedia, Super prime.

Crossrefs

Cf. A000040, A006450, A330653, A007953, A040115, A053392, A046704.