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

10253, 35201, 121921, 129121, 155851, 158551, 712909, 909217, 1005761, 1007921, 1010201, 1013321, 1020101, 1020881, 1032131, 1037801, 1084357, 1087301, 1100441, 1115399, 1233101, 1297001, 1312301, 1440011, 1564991, 1675001, 1880201, 1963369, 1994651, 7534801, 9633691, 9935111, 10000609, 10005361

Offset: 1

Author

J. M. Bergot and Robert Israel, Sep 08 2022

Keywords

• nonn
• base

Comments

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.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..600

Crossrefs

Cf. A004086, A006567, A007953, A356947.

Programs

Maple

filter:= proc(n) local L, i, r, s;
  if not isprime(n) then return false fi;
  L:= convert(n, base, 10);
  r:= add(L[-i]*10^(i-1), i=1..nops(L));
  if r = n or not isprime(r) then return false fi;
  s:= convert(L, `+`);
  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
end proc:
select(filter, [seq(i,i=3..10^7,2)]);