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 A377270 #52 Nov 29 2024 21:38:40 %S A377270 1,1,1,2,3,7,6,14,33,48,24,106,51,240,362,305,251,1269,1047,1752,2456, %T A377270 3773,3121,8959,39089,62223,33299,177305,42613,238782,373418,699763, %U A377270 916051,2715933,2256419,13103923,7100513,16902825,13833549,11323041,66402079,54299882 %N A377270 Smallest index k such that the k-th prime number in base-2 contains the n-th Fibonacci number in base-2 as a contiguous substring. %C A377270 The intersections between this sequence and similar sequences in base-B occur at values of n that are the indices of prime Fibonacci numbers, and values of a(n) such that the a(n)-th prime number is a Fibonacci number. %H A377270 Daniel Suteu, <a href="/A377270/b377270.txt">Table of n, a(n) for n = 1..88</a> %H A377270 Charles Marsden, <a href="/A377270/a377270_4.py.txt">Python program</a> %F A377270 a(n) = A377483(A000045(n)). - _Pontus von Brömssen_, Nov 29 2024 %e A377270 For n=1, fib(1)=1 -> 1 in base-2. The first prime containing 1 in its base-2 form is P(1)=2 -> 10. Therefore, a(1)=1. %e A377270 For n=4, fib(4)=3 -> 11 in base-2. The first prime containing 11 in its base-2 form is P(2)=3 -> 11. Therefore, a(4)=2. %e A377270 For n=6, fib(6)=8 -> 1000 in base-2. The first prime containing 1000 in its base-2 form is P(7)=17 -> 10001. Therefore, a(6)=7. %t A377270 s={}; Do[k=0; Until[SequenceCount[IntegerDigits[Prime[k], 2], IntegerDigits[Fibonacci[n], 2]]>0, k++]; AppendTo[s, k], {n, 31}]; s (* _James C. McMahon_, Nov 21 2024 *) %o A377270 (Python) # See links. %o A377270 (Python) %o A377270 from sympy import fibonacci, nextprime, primepi %o A377270 def A377270(n): %o A377270 f = fibonacci(n) %o A377270 p, k, a = nextprime(f-1), primepi(f-1)+1, bin(f)[2:] %o A377270 while True: %o A377270 if a in bin(p)[2:]: %o A377270 return k %o A377270 p = nextprime(p) %o A377270 k += 1 # _Chai Wah Wu_, Nov 20 2024 %o A377270 (Sidef) %o A377270 for n in (1..35) { %o A377270 var bin = n.fib.as_bin %o A377270 var min = Inf %o A377270 for k in (0..Inf) { %o A377270 ['0','1'].variations_with_repetition(k, {|*a| %o A377270 [a..., bin].variations(a.len+1, {|*t| %o A377270 var m = Num(t.join, 2) %o A377270 if (m.is_prime && m.as_bin.contains(bin)) { %o A377270 min = m if (m < min) %o A377270 } %o A377270 }) %o A377270 }) %o A377270 break if (min < Inf) %o A377270 } %o A377270 print(min.primepi, ", ") %o A377270 } # _Daniel Suteu_, Nov 02 2024 %Y A377270 Cf. A000040, A000045, A001605, A004676, A099000, A377483. %K A377270 nonn,base %O A377270 1,4 %A A377270 _Charles Marsden_, Oct 22 2024 %E A377270 a(36)-a(42) from _Daniel Suteu_, Nov 02 2024