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A356979
Emirps p such that p, its digit reversal, and their squares are all quasi-Niven numbers.
1
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
1,1
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
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
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Sep 08 2022
STATUS
approved