This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A292472 #14 Jan 05 2025 19:51:41 %S A292472 0,1,13,34,55 %N A292472 Generalized heptagonal numbers that are also Fibonacci numbers. %C A292472 Intersection of A000045 and A085787. %C A292472 Exactly five such numbers exist (cf. Srinivasa Rao, 2003). %C A292472 All (generalized) g-gonal numbers in Fibonacci sequences up to g=20 have been determined (cf. Tengely, 2009). - _Tomohiro Yamada_, Sep 26 2017 %H A292472 B. Srinivasa Rao, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/41-5/rao.pdf">Heptagonal Numbers in Fibonacci Sequence and Diophantine Equations 4x^2 = 5y^2(5y-3)^2+-16</a>, The Fibonacci Quarterly, Vol. 41, No. 5 (2003), 414-420. %H A292472 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 (2009), 235-240. %t A292472 Intersection[Array[(# (# + 1)/2 - 1)/5 &, 50, 0], Array[Fibonacci, 50, 0]] (* _Michael De Vlieger_, Sep 18 2017 *) %o A292472 (PARI) a085787(n) = (5*(-n\2)^2 - (-n\2)*3*(-1)^n) / 2 %o A292472 is_a000045(n) = my(x=0); while(fibonacci(x) < n, x++); if(fibonacci(x)==n, return(1)); 0 %o A292472 for(n=0, 60, if(is_a000045(a085787(n)), print1(a085787(n), ", "))) %Y A292472 Cf. A000045, A085787. %Y A292472 Cf. A292850 (Generalized heptagonal Lucas numbers). %K A292472 nonn,easy,fini,full %O A292472 1,3 %A A292472 _Felix Fröhlich_, Sep 17 2017