A045725 Fibonacci numbers having initial digit '1'.

1, 13, 144, 1597, 10946, 17711, 121393, 196418, 1346269, 14930352, 102334155, 165580141, 1134903170, 1836311903, 12586269025, 139583862445, 1548008755920, 10610209857723, 17167680177565, 117669030460994, 190392490709135, 1304969544928657, 14472334024676221, 160500643816367088

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• base

Crossrefs

Cf. A105501.

Intersection of A000045 and A131835.

Programs

Magma

[Fibonacci(n): n in [2..100] | Intseq(Fibonacci(n))[#Intseq(Fibonacci(n))] eq 1]; // Vincenzo Librandi, Jan 30 2019

Mathematica

Select[Fibonacci[Range[2, 100]], IntegerDigits[#, 10][[1]] == 1 &] (* T. D. Noe, Nov 01 2006 *)

PARI

select(x->(digits(x)[1] == 1), vector(85, n, fibonacci(n+1))) \\ Michel Marcus, Jan 30 2019

Scala

def fibonacci(n: BigInt): BigInt = {
  val zero = BigInt(0)
  def fibTail(n: BigInt, a: BigInt, b: BigInt): BigInt = n match {
    case `zero` => a
    case _ => fibTail(n - 1, b, a + b)
  }
  fibTail(n, 0, 1)
} // Tail recursion by Dario Carrrasquel
((2 to 100).map(fibonacci())).filter(.toString.startsWith("1")) // Alonso del Arte, Apr 22 2019

Extensions

Corrected by T. D. Noe, Nov 01 2006