A113193 -id:A113193 - cp's OEIS frontend

A113194 Numbers k such that Lucas(k) - Lucas(i) is composite for i=0..k-3.

5, 7, 10, 17, 19, 23, 29, 31, 34, 41, 44, 49, 53, 55, 57, 62, 67, 68, 71, 75, 77, 79, 80, 87, 89, 93, 98, 100, 101, 103, 107, 109, 110, 116, 122, 124, 125, 133, 134, 135, 136, 143, 147, 154, 155, 160, 161, 164, 167, 170, 173, 177, 180, 184, 185, 188, 190, 194, 196

Offset: 1

T. D. Noe, Oct 17 2005

nonn

These are the numbers k such that A113193(k) = 0.

Robert Israel, Table of n, a(n) for n = 1..2600

Cf. A000032, A113192 (primes that are the difference of two Lucas numbers).

Cf. A113193.

Luc:= 2,1,3: R:= NULL: count:= 0:
a:= 1: b:= 3:
for n from 3 while count < 100 do
  c:= a+b; a:= b; b:=c; Luc:= Luc,c;
  if ormap(isprime, [seq(c-Luc[i],i=1..n-2)]) then next fi;
  R:= R, n; count:= count+1;
od:
R; # Robert Israel, Jan 18 2023

Mathematica
```
lst={}; Do[i=0; While[i
				
```

A113192 Primes that are the difference of two Lucas numbers; primes in A113191.

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 29, 43, 47, 73, 181, 197, 199, 293, 311, 503, 521, 839, 1361, 2131, 2203, 2207, 3571, 5749, 9349, 13763, 23633, 24469, 24473, 38239, 103483, 103681, 161983, 167759, 271367, 399601, 439081, 439157, 709283, 1692737, 3010349

Offset: 1

T. D. Noe, Oct 17 2005

nonn

The difference L(i)-L(j) equals the sum L(j+1)+...+L(i+2).

			The prime 181 is here because it is L(11)-L(6).

T. D. Noe, Table of n, a(n) for n=1..1000

Cf. A000032 (Lucas numbers), A001606 (Lucas(n) is prime), A113193 (number of times that Lucas(n)-Lucas(i) is prime for i=0..n-3).

Lucas[n_] := Fibonacci[n+1]+Fibonacci[n-1]; lst={}; Do[p=Lucas[n]-Lucas[i]; If[PrimeQ[p], AppendTo[lst, p]], {n, 2, 40}, {i, 0, n-2}]; Union[lst]

cp's OEIS Frontend

A113194 Numbers k such that Lucas(k) - Lucas(i) is composite for i=0..k-3.

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