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Smallest triangular number > 1 and == 1 (mod prime(n)).
1

%I #14 Jan 01 2024 13:09:09

%S 3,10,6,15,45,66,120,153,231,378,435,630,780,861,1035,1326,1653,1770,

%T 2145,2415,2556,3003,3321,3828,4560,4950,5151,5565,5778,6216,7875,

%U 8385,9180,9453,10878,11175,12090,13041,13695,14706,15753,16110,17955,18336

%N Smallest triangular number > 1 and == 1 (mod prime(n)).

%H Robert Israel, <a href="/A087397/b087397.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (prime(n)-2)*(prime(n)-1)/2 for n >= 3.

%e a(7) = 120 == 1 (mod 17), prime (7) = 17.

%p 3,10, seq((ithprime(i)-2)*(ithprime(i)-1)/2, i=3..50); # _Robert Israel_, Dec 23 2018

%t Join[{3, 10}, Table[(Prime[n] - 2) (Prime[n] - 1) / 2, {n, 3, 50}]] (* _Vincenzo Librandi_, Dec 24 2018 *)

%o (Magma) [3,10] cat [(NthPrime(n)-2)*(NthPrime(n)-1)/2: n in [3..50]]; // _Vincenzo Librandi_, Dec 24 2018

%K nonn

%O 1,1

%A _Amarnath Murthy_, Sep 10 2003

%E More terms from _David Wasserman_, Jun 01 2005

%E Edited by _Robert Israel_, Dec 23 2018