A048593 Converse numbers: composite Fibonacci numbers Fib(k) that are congruent to Legendre symbol (k/5) mod k.

4181, 75025, 1346269, 24157817, 165580141, 53316291173, 956722026041, 1548008755920, 2504730781961, 44945570212853, 308061521170129, 806515533049393, 14472334024676221, 1779979416004714189, 83621143489848422977, 573147844013817084101, 1500520536206896083277, 10284720757613717413913

Offset

1,1

References

Joe Roberts, Lure of the Integers, "Integer 4181". (There is a misprint in the definition.)

Links

Robert Israel, Table of n, a(n) for n = 1..670

Example

4181 is the 19th Fibonacci number, it is composite and it is congruent to (19/5) mod 19, so 4181 is a term.

Maple

a:= 1: b:= 1: R:= NULL: count:= 0:
for n from 3 while count < 50 do
  t:= a; a:= b; b:= t+b;
  if b - NumberTheory:-LegendreSymbol(n, 5) mod n = 0 and not isprime(b) then
     R:= R, b; count:= count+1;
  fi
od:
R; # Robert Israel, Jul 19 2023

Crossrefs

Cf. A000045, A080891.

Sequence in context: A238082 A072322 A045728 * A358555 A050937 A135953

Adjacent sequences: A048590 A048591 A048592 * A048594 A048595 A048596

Keyword

nonn

Author

Jud McCranie

Extensions

Corrected by Robert Israel, Jul 19 2023

Status

approved