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

1,1

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.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Wikipedia, Super prime.

Example

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.

Crossrefs

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

Sequence in context: A141898 A054998 A067378 * A171138 A071886 A276302

Adjacent sequences: A331028 A331029 A331030 * A331032 A331033 A331034

Keyword

nonn,base

Author

Scott R. Shannon, Jan 07 2020

Status

approved