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A356979 Emirps p such that p, its digit reversal, and their squares are all quasi-Niven numbers.

%I A356979 #37 Sep 09 2022 10:02:47
%S A356979 10253,35201,121921,129121,155851,158551,712909,909217,1005761,
%T A356979 1007921,1010201,1013321,1020101,1020881,1032131,1037801,1084357,
%U A356979 1087301,1100441,1115399,1233101,1297001,1312301,1440011,1564991,1675001,1880201,1963369,1994651,7534801,9633691,9935111,10000609,10005361
%N A356979 Emirps p such that p, its digit reversal, and their squares are all quasi-Niven numbers.
%C A356979 Primes p such that the digit reversal R(p) is another prime, and p mod A007953(p) = R(p) mod A007953(R(p)) = p^2 mod A007953(p^2) = R(p)^2 mod A007953(R(p)^2) = 1.
%H A356979 Robert Israel, <a href="/A356979/b356979.txt">Table of n, a(n) for n = 1..600</a>
%e A356979 a(3) = 121921 is a term because it and its reversal 129121 are distinct primes, 121921 mod (1+2+1+9+2+1) = 129121 mod (1+2+9+1+2+1) = 1, 121921^2 = 14864730241 with sum of digits 40, 129121^2 = 16672232641 also with sum of digits 40, 121921^2 mod 40 = 1 and 129121^2 mod 40 = 1.
%p A356979 filter:= proc(n) local L, i, r, s;
%p A356979   if not isprime(n) then return false fi;
%p A356979   L:= convert(n, base, 10);
%p A356979   r:= add(L[-i]*10^(i-1), i=1..nops(L));
%p A356979   if r = n or not isprime(r) then return false fi;
%p A356979   s:= convert(L, `+`);
%p A356979   n mod s = 1 and r mod s = 1 and n^2 mod convert(convert(n^2,base,10),`+`)=1 and r^2 mod convert(convert(r^2,base,10),`+`)=1
%p A356979 end proc:
%p A356979 select(filter, [seq(i,i=3..10^7,2)]);
%Y A356979 Cf. A004086, A006567, A007953, A356947.
%K A356979 nonn,base
%O A356979 1,1
%A A356979 _J. M. Bergot_ and _Robert Israel_, Sep 08 2022