A353064 Numbers simultaneously square and heptagonal pyramidal.

0, 1, 196, 99225

Offset: 1

Author

Kelvin Voskuijl, Apr 21 2022

Keywords

• nonn
• more

Comments

Is this sequence finite?

No other terms < 10^32. - Michael S. Branicky, Jul 12 2022

Examples

			196 is a term because 196 = 14^2 is a perfect square and 196 = 6*(6+1)*(5*6-2)/6 is the 6th heptagonal pyramidal number.
		

Links

• ProofWiki, Heptagonal Pyramidal Numbers which are Square

Crossrefs

Intersection of A000290 and A002413.

Cf. A003556 (tetrahedral and square), 1 and 4900 are only squares that are square pyramidal, A277792 (pentagonal pyramidal and square).

Programs

Maple

select(issqr, [seq(n*(n+1)*(5*n-2)/6, n=0..50)])[];  # Alois P. Heinz, Apr 21 2022

Mathematica

Select[Table[n*(n + 1)*(5*n - 2)/6, {n, 0, 100}], IntegerQ @ Sqrt[#] &] (* Amiram Eldar, Apr 21 2022 *)