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Lucas numbers that are also generalized heptagonal numbers.
1

%I #12 Jan 05 2025 19:51:41

%S 1,4,7,18

%N Lucas numbers that are also generalized heptagonal numbers.

%C Intersection of A000032 and A085787.

%C Except 4, these are also ordinary heptagonal numbers.

%C All terms are shown, as confirmed by Srinivasa Rao (2002).

%C All (generalized) g-gonal numbers in Lucas sequences up to g=20 have been determined, see Tengely (2009).

%H B. Srinivasa Rao, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/40-4/rao.pdf">Heptagonal Numbers in the Lucas Sequence and Diophantine Equations x^2(5x-3)^2 = 20y^2+-16</a>, The Fibonacci Quarterly, Vol. 40, No. 4 (2002), 319-322.

%H Szabolcs Tengely, <a href="http://shrek.unideb.hu/~tengely/G-gonal-FQ.pdf">Finding g-gonal numbers in recurrence sequences</a>, Fibonacci Quarterly, vol.46/47, no.3, pp.235-240, (2009).

%Y Cf. A000032, A085787.

%Y Cf. A248506 (triangular Lucas Numbers).

%K nonn,easy,full,fini

%O 1,2

%A _Tomohiro Yamada_, Sep 25 2017