A283225 Primes prime(k) such that prime(k)^2 mod prime(k+2) is different from prime(k+2)^2 mod prime(k).

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 43, 47, 53, 59, 61, 73, 79, 83, 89, 109, 113, 137, 139, 199, 211, 241, 283, 293, 313, 317, 523, 1321, 1327

Offset: 1

Author

Arnaud Vernier, Mar 03 2017

Keywords

• more
• nonn

Comments

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

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).

If it exists, then a(35) > 10^12. - Lucas A. Brown, Feb 11 2021

Examples

			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.
		

Crossrefs

Cf. A124129.

Programs

Mathematica

Select[Prime[Range[250]],PowerMod[#,2,NextPrime[#,2]] != PowerMod[ NextPrime[ #,2],2,#]&]  (* Harvey P. Dale, Nov 17 2020 *)