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

1,1

Comments

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

Links

Table of n, a(n) for n=1..53.

Example

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

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)

Crossrefs

A000217 A117112 A145016

Sequence in context: A038963 A167609 A117112 * A233414 A233863 A371065

Adjacent sequences: A145029 A145030 A145031 * A145033 A145034 A145035

Keyword

nonn

Author

Vladimir Shevelev, Sep 30 2008

Extensions

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

Status

approved