A292472 Generalized heptagonal numbers that are also Fibonacci numbers.

0, 1, 13, 34, 55

Offset

1,3

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

Table of n, a(n) for n=1..5.

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.

Mathematica

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

Prog

(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), ", ")))

Crossrefs

Cf. A000045, A085787.

Cf. A292850 (Generalized heptagonal Lucas numbers).

Sequence in context: A245170 A134864 A093100 * A081271 A190458 A180673

Adjacent sequences: A292469 A292470 A292471 * A292473 A292474 A292475

Keyword

nonn,easy,fini,full

Author

Felix Fröhlich, Sep 17 2017

Status

approved