OFFSET
1,2
COMMENTS
Start of 3 consecutive terms in A057128. All terms are congruent to {1, 2} mod 5 and {0, 1, 2} mod 6.
If k is a term of this sequence then -3 is a quadratic residue modulo k*(k + 1)*(k + 2)/2, but the converse is not true if k, (k + 1)/2 and k + 2 are terms in A057128 and k == 7 (mod 16) (k = 487, 631, 2071, ...).
EXAMPLE
12 is a term since 3^2 == -3 (mod 12), 6^2 == -3 (mod 13) and 5^2 == -3 (mod 14).
PROG
(PARI) isA057128(n) = issquare(Mod(-3, n));
isA305864(n) = isA057128(n)&&isA057128(n+1)&&isA057128(n+2);
for(n=1, 10000, if(isA305864(n), print1(n, ", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Aug 06 2018
STATUS
approved