A329527 The prime numbers that are prime-indexed primes and whose reversal, digit sum, sum of digits to their own power, adjacent digit sum concatenation, and adjacent digit difference concatenation are also primes.

10180481, 11245547, 18486581, 35015063, 72042701, 72466367, 112823743, 113135621, 171199663, 304000381, 308486107, 318827167, 370257067, 382355443, 722948621, 731621629, 765348167, 771649421, 775786489, 776751581, 916132267, 963985829, 965521463, 980165701, 1002471581

Offset

1,1

Comments

This sequence lists the prime numbers that are prime-indexed primes A006450, and whose digit reversal A004086, digit sum A007953, sum of digits to their own powers A045503, concatenation of adjacent digit sums A053392, and concatenation of adjacent digit differences A040115, are also primes. This is a subsequence of A006450 and A331031. Note that, as in A045503, we assume 0^0 = 1. There are only three entries for primes up to 20491057.

Links

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

Wikipedia, Super prime.

Example

a(1) = 10180481, as 10180481 is the 675797th prime, 10180481 in reversal is 18408101, 1+0+1+8+0+4+8+1=23, 1^1+0^0+1^1+8^8+0^0+4^4+8^8+1^1=33554693, '1+0'+'0+1'+'1+8'+'8+0'+'0+4'+'4+8'+'8+1'=11984129, '|1-0|'+'|0-1|'+'|1-8|'+'|8-0|'+'|0-4|'+'|4-8|'+'|8-1|'=1178447, and 10180481, 675797, 18408101, 23, 33554693, 11984129, 1178447 are all prime.

Crossrefs

Cf. A000040, A006450, A330653, A331031, A007953, A040115, A053392, A046704, A007500, A045503, A004086.

Sequence in context: A244076 A234404 A034635 * A325607 A282873 A219743

Adjacent sequences: A329524 A329525 A329526 * A329528 A329529 A329530

Keyword

nonn,base

Author

Scott R. Shannon, Jan 07 2020

Extensions

Terms a(4) and beyond from Giovanni Resta, Jan 08 2020

Status

approved