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Triangular numbers equal to the difference between a prime number and its index.
2

%I #4 Jun 28 2012 12:13:32

%S 1,3,6,10,28,105,120,153,231,465,496,1081,1378,1485,1653,1711,2628,

%T 3003,3081,3160,4950,5050,5460,6670,6903,8001,8778,10296,11781,14028,

%U 15225,16290,19701,20503,21528,21945,22155,24310,24531,25200,27495

%N Triangular numbers equal to the difference between a prime number and its index.

%H Harvey P. Dale, <a href="/A115887/b115887.txt">Table of n, a(n) for n = 1..500</a>

%e 28=T(7)=p(13)-13.

%t Union[Select[Table[Prime[i]-i,{i,20000}],IntegerQ[Sqrt[8#+1]]&]] (* _Harvey P. Dale_, Jun 28 2012 *)

%Y Cf. A115883.

%K nonn

%O 1,2

%A _Giovanni Resta_, Feb 06 2006