The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A321612 Numbers k such that all k - t are triangular numbers where t is a triangular number in range k/2 <= t < k. 0
2, 4, 6, 7, 9, 13, 16, 21, 31 (list; graph; refs; listen; history; text; internal format)



The following is a quotation from Hage-Hassan in his paper (see Link below). "The (concept of) right and left symmetry is fundamental in physics. This incites us to ask whether this symmetry is in (the) primes. Find the numbers n with a + a' = n. a, a' are primes and {a} are all the primes with: n/2 ≤ a <n and n = 2,3, ..."

This sequence is analogous to A320447. Instead of the sequence of primes it uses the sequence of triangular numbers (A000217). It is conjectured that the sequence is finite and full.


Table of n, a(n) for n=1..9.

Mehdi Hage-Hassan, An elementary introduction to Quantum mechanic, hal-00879586 2013 pp 58.


a(9) = 31, because the triangular numbers in the range 16 <= p < 31 are {21}. Also the complementary set {10} has all its members triangular numbers. This is the 9th occurrence of such a number.


TriangularQ[n_] := Module[{m=0}, While[n>m(m+1)/2, m++]; If[n==m(m+1)/2, True, False]]; plst[n_] := Select[Range[Ceiling[n/2], n-1], TriangularQ]; lst={}; Do[If[plst[n]!={}&&AllTrue[n-plst[n], TriangularQ], AppendTo[lst, n]], {n, 1, 200}]; lst


Cf. A000217, A320447.

Sequence in context: A186708 A227697 A097457 * A259983 A050095 A102528

Adjacent sequences:  A321609 A321610 A321611 * A321613 A321614 A321615




Frank M Jackson, Dec 18 2018



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 12 09:53 EDT 2021. Contains 343821 sequences. (Running on oeis4.)