This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A347905 #10 Sep 20 2021 11:50:03 %S A347905 2,2,2,3,0,3,2,2,2,2,3,0,0,0,3,2,2,2,2,2,2,4,0,3,0,3,0,4,3,5,0,4,3,0, %T A347905 3,4,3,0,3,0,0,0,3,0,3,2,2,2,2,2,2,2,2,2,2,3,0,0,0,3,0,3,0,0,0,3,2,2, %U A347905 2,2,2,2,2,2,2,2,2,2,4,0,6,0,3,0,0,0,3,0,3,0,4 %N A347905 Array read by antidiagonals, m, n >= 1: T(m,n) is the position of the first prime (after the two initial terms) in the Fibonacci-like sequence with initial terms m and n, or 0 if no such prime exists. %C A347905 There are cases where T(m,n) = 0 even when m and n are coprime; see A082411, A083104, A083105, A083216, and A221286. %C A347905 The largest value of T(m,n) for m, n <= 5000 is T(1591,300) = 17262. %F A347905 T(m,n) = 0 if m and n have a common factor. %F A347905 T(m,n) = T(n,m+n) + 1 if m+n is not prime, otherwise T(m,n) = 2. %e A347905 Array begins: %e A347905 m\n| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 %e A347905 ---+------------------------------------------------------------ %e A347905 1 | 2 2 3 2 3 2 4 3 3 2 3 2 4 3 3 2 4 2 4 3 %e A347905 2 | 2 0 2 0 2 0 5 0 2 0 2 0 4 0 2 0 2 0 4 0 %e A347905 3 | 3 2 0 2 3 0 3 2 0 2 6 0 3 2 0 2 3 0 3 2 %e A347905 4 | 2 0 2 0 4 0 2 0 2 0 4 0 2 0 2 0 4 0 2 0 %e A347905 5 | 3 2 3 3 0 2 3 2 3 0 4 2 3 2 0 3 4 2 3 0 %e A347905 6 | 2 0 0 0 2 0 2 0 0 0 2 0 2 0 0 0 2 0 5 0 %e A347905 7 | 4 3 3 2 3 2 0 3 4 2 3 2 4 0 3 2 3 3 4 3 %e A347905 8 | 4 0 2 0 2 0 4 0 2 0 2 0 5 0 2 0 4 0 4 0 %e A347905 9 | 3 2 0 2 3 0 3 2 0 2 3 0 6 2 0 3 3 0 3 2 %e A347905 10 | 2 0 2 0 0 0 2 0 2 0 4 0 2 0 0 0 4 0 2 0 %e A347905 11 | 3 2 3 3 4 2 4 2 3 3 0 2 3 5 3 3 4 2 4 2 %e A347905 12 | 2 0 0 0 2 0 2 0 0 0 2 0 5 0 0 0 2 0 2 0 %e A347905 13 | 4 3 3 2 3 2 4 3 3 2 4 3 0 3 3 2 3 2 4 3 %e A347905 14 | 4 0 2 0 2 0 0 0 2 0 4 0 4 0 2 0 2 0 5 0 %e A347905 15 | 3 2 0 2 0 0 3 2 0 0 3 0 3 2 0 2 6 0 3 0 %e A347905 16 | 2 0 2 0 4 0 2 0 4 0 5 0 2 0 2 0 4 0 4 0 %e A347905 17 | 3 2 3 5 10 2 3 6 4 3 4 2 3 2 3 5 0 3 7 2 %e A347905 18 | 2 0 0 0 2 0 5 0 0 0 2 0 2 0 0 0 5 0 2 0 %e A347905 19 | 4 3 4 2 3 3 4 5 3 2 3 2 6 3 4 5 3 2 0 3 %e A347905 20 | 4 0 2 0 0 0 4 0 2 0 2 0 4 0 0 0 2 0 4 0 %e A347905 T(2,7) = 5, because 5 is the smallest k >= 2 for which A022113(k) is prime. %o A347905 (Python) %o A347905 # Note that in the (rare) case when m and n are coprime but there are no primes in the Fibonacci-like sequence, this function will go into an infinite loop. %o A347905 from sympy import isprime,gcd %o A347905 def A347905(m,n): %o A347905 if gcd(m,n) != 1: %o A347905 return 0 %o A347905 m,n = n,m+n %o A347905 k=2 %o A347905 while not isprime(n): %o A347905 m,n = n,m+n %o A347905 k += 1 %o A347905 return k %Y A347905 Cf. A022113, A082411, A083104, A083105, A083216, A221286, A347904. %K A347905 nonn,tabl %O A347905 1,1 %A A347905 _Pontus von Brömssen_, Sep 18 2021