A292472 Generalized heptagonal numbers that are also Fibonacci numbers.

0, 1, 13, 34, 55

Offset: 1

Author

Felix Fröhlich, Sep 17 2017

Keywords

• nonn
• easy
• fini
• full

Comments

Intersection of A000045 and A085787.

Exactly five such numbers exist (cf. Srinivasa Rao, 2003).

All (generalized) g-gonal numbers in Fibonacci sequences up to g=20 have been determined (cf. Tengely, 2009). - Tomohiro Yamada, Sep 26 2017

Links

• B. Srinivasa Rao, Heptagonal Numbers in Fibonacci Sequence and Diophantine Equations 4x^2 = 5y^2(5y-3)^2+-16, The Fibonacci Quarterly, Vol. 41, No. 5 (2003), 414-420.
• Szabolcs Tengely, Finding g-gonal numbers in recurrence sequences, Fibonacci Quarterly, Vol.46/47, No. 3 (2009), 235-240.

Crossrefs

Cf. A000045, A085787.

Cf. A292850 (Generalized heptagonal Lucas numbers).

Programs

Mathematica

Intersection[Array[(# (# + 1)/2 - 1)/5 &, 50, 0], Array[Fibonacci, 50, 0]] (* Michael De Vlieger, Sep 18 2017 *)

PARI

a085787(n) = (5*(-n\2)^2 - (-n\2)*3*(-1)^n) / 2
is_a000045(n) = my(x=0); while(fibonacci(x) < n, x++); if(fibonacci(x)==n, return(1)); 0
for(n=0, 60, if(is_a000045(a085787(n)), print1(a085787(n), ", ")))