A356979 - OEIS

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

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OFFSET

1,1

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.

LINKS

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

EXAMPLE

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.

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)]);

CROSSREFS

Cf. A004086, A006567, A007953, A356947.