A283225 - OEIS

%I #22 Feb 12 2021 01:34:39

%S 2,3,5,7,11,13,17,19,23,29,31,43,47,53,59,61,73,79,83,89,109,113,137,

%T 139,199,211,241,283,293,313,317,523,1321,1327

%N Primes prime(k) such that prime(k)^2 mod prime(k+2) is different from prime(k+2)^2 mod prime(k).

%C I conjecture that there are no other terms in this sequence.

%C A124129 is constructed in a similar way: by comparing the values of prime(k)^2 mod prime(k+1) and prime(k+1)^2 mod prime(k).

%C If it exists, then a(35) > 10^12. - _Lucas A. Brown_, Feb 11 2021

%e a(10) = prime(10) = 29 is in the sequence because the remainder of the division of 29^2 = 841 by prime(12) = 37 is 27, which is different from the remainder of the division of 37^2 = 1369 by prime(10) = 29, which is 6.

%t Select[Prime[Range[250]],PowerMod[#,2,NextPrime[#,2]] != PowerMod[ NextPrime[ #,2],2,#]&]  (* _Harvey P. Dale_, Nov 17 2020 *)

%Y Cf. A124129.

%K more,nonn

%O 1,1

%A _Arnaud Vernier_, Mar 03 2017