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.

2, 3, 7, 11, 13, 29, 31, 37, 61, 67, 79, 97, 101, 137, 139, 151, 163, 181, 191, 193, 211, 241, 263, 277, 331, 379, 409, 421, 463, 499, 571, 601, 631, 709, 739, 751, 769, 821, 823, 947, 967, 991, 1063, 1087, 1091, 1109, 1117, 1129, 1231, 1303, 1327, 1381, 1399

Offset: 1

Author

Vladimir Shevelev, Sep 30 2008

Keywords

• nonn

Comments

Primes p for which p-A057944(p) is in A000217. [From R. J. Mathar, Oct 25 2010]

Examples

			E. g., t(181)=171 (see A000217) and 181-171=10 is triangular number. Therefore p=181 is in the sequence
		

Crossrefs

A000217 A117112 A145016

Programs

Maple

Contribution from R. J. Mathar, Oct 25 2010: (Start)
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:
isA000217 := proc(n) issqr(8*n+1) ; end proc:
isA145032 := proc(p) if isprime(p) then tres := p-A057944(p) ; isA000217(tres) ; else false; end if; end proc:
for n from 1 to 400 do p := ithprime(n) ; if isA145032(p) then printf("%d,",p) ; end if; end do: (End)

Extensions

More terms from R. J. Mathar, Oct 25 2010