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

1,1

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

Links

Table of n, a(n) for n=1..34.

Example

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.

Mathematica

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

Crossrefs

Cf. A124129.

Sequence in context: A178762 A051750 A268109 * A100724 A257658 A182231

Adjacent sequences: A283222 A283223 A283224 * A283226 A283227 A283228

Keyword

more,nonn

Author

Arnaud Vernier, Mar 03 2017

Status

approved