A329527 - OEIS

%I #35 Mar 31 2024 17:10:45

%S 10180481,11245547,18486581,35015063,72042701,72466367,112823743,

%T 113135621,171199663,304000381,308486107,318827167,370257067,

%U 382355443,722948621,731621629,765348167,771649421,775786489,776751581,916132267,963985829,965521463,980165701,1002471581

%N 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.

%C 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.

%H Giovanni Resta, <a href="/A329527/b329527.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Super-prime">Super prime</a>.

%e 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.

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

%K nonn,base

%O 1,1

%A _Scott R. Shannon_, Jan 07 2020

%E Terms a(4) and beyond from _Giovanni Resta_, Jan 08 2020