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A283225
Primes prime(k) such that prime(k)^2 mod prime(k+2) is different from prime(k+2)^2 mod prime(k).
0
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
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
KEYWORD
more,nonn
AUTHOR
Arnaud Vernier, Mar 03 2017
STATUS
approved