cp's OEIS Frontend

A145032 If t(n) is the maximal triangular number not exceeding n, then a(n) is the n-th prime for which a(n)-t(a(n)) is a triangular number.

%I A145032 #6 Jul 22 2025 06:12:21
%S A145032 2,3,7,11,13,29,31,37,61,67,79,97,101,137,139,151,163,181,191,193,211,
%T A145032 241,263,277,331,379,409,421,463,499,571,601,631,709,739,751,769,821,
%U A145032 823,947,967,991,1063,1087,1091,1109,1117,1129,1231,1303,1327,1381,1399
%N A145032 If t(n) is the maximal triangular number not exceeding n, then a(n) is the n-th prime for which a(n)-t(a(n)) is a triangular number.
%C A145032 Primes p for which p-A057944(p) is in A000217. [From _R. J. Mathar_, Oct 25 2010]
%e A145032 E. g., t(181)=171 (see A000217) and 181-171=10 is triangular number. Therefore p=181 is in the sequence
%p A145032 Contribution from _R. J. Mathar_, Oct 25 2010: (Start)
%p A145032 A057944 := proc(n) for i from 0 do if i*(i+1)/2 > n then return (i-1)*i /2 ; end if; end do: end proc:
%p A145032 isA000217 := proc(n) issqr(8*n+1) ; end proc:
%p A145032 isA145032 := proc(p) if isprime(p) then tres := p-A057944(p) ; isA000217(tres) ; else false; end if; end proc:
%p A145032 for n from 1 to 400 do p := ithprime(n) ; if isA145032(p) then printf("%d,",p) ; end if; end do: (End)
%Y A145032 A000217 A117112 A145016
%K A145032 nonn
%O A145032 1,1
%A A145032 _Vladimir Shevelev_, Sep 30 2008
%E A145032 More terms from _R. J. Mathar_, Oct 25 2010