cp's OEIS Frontend

A352942 Let p = prime(n); a(n) = number of primes q with same number of binary digits as p that can be obtained from p by changing one binary digit.

%I A352942 #112 Apr 23 2025 19:53:13
%S A352942 1,1,1,1,0,0,1,2,2,1,2,1,1,3,1,2,1,1,2,3,1,1,1,1,2,3,2,0,1,1,0,2,1,2,
%T A352942 3,1,1,4,1,0,1,1,0,1,3,1,0,0,1,1,0,0,0,0,0,1,2,2,0,3,2,1,1,2,2,1,1,0,
%U A352942 3,0,0,2,2,0,2,2,2,3,2,2,0,2,0,1,2,0,1
%N A352942 Let p = prime(n); a(n) = number of primes q with same number of binary digits as p that can be obtained from p by changing one binary digit.
%C A352942 a(n) is also the degree of prime(n) in the graph P(A070939(prime(n)), 2), defined in A145667.
%H A352942 Paolo Xausa, <a href="/A352942/b352942.txt">Table of n, a(n) for n = 1..10000</a>
%F A352942 a(n) = deg(prime(n)) in P(A070939(prime(n)), 2) (see A145667).
%e A352942 prime(1) = 2, in binary 10, has one neighbor 11 in P(2, 2), so a(1) = 1.
%e A352942 prime(14) = 43, in binary 101011, has neighbors 101001 (41), 101111 (47), 111011 (59), so a(14) = 3.
%p A352942 a:= n-> (p-> nops(select(isprime, {seq(Bits[Xor]
%p A352942         (p, 2^i), i=0..ilog2(p)-1)})))(ithprime(n)):
%p A352942 seq(a(n), n=1..100);  # _Alois P. Heinz_, May 11 2022
%t A352942 A352942[n_] := Count[BitXor[#, 2^Range[0, BitLength[#] - 2]], _?PrimeQ] & [Prime[n]];
%t A352942 Array[A352942, 100] (* _Paolo Xausa_, Apr 23 2025 *)
%o A352942 (Python)
%o A352942 from sympy import isprime, sieve
%o A352942 def neighs(s):
%o A352942     digs = "01"
%o A352942     ham1 = (s[:i]+d+s[i+1:] for i in range(len(s)) for d in digs if d!=s[i])
%o A352942     yield from (h for h in ham1 if h[0] != '0')
%o A352942 def a(n):
%o A352942     return sum(1 for s in neighs(bin(sieve[n])[2:]) if isprime(int(s, 2)))
%o A352942 print([a(n) for n in range(1, 88)])
%Y A352942 Binary analog of A125002.
%Y A352942 Cf. A000040, A004676, A070939, A104080, A014234, A137985, A145667, A353738.
%K A352942 nonn,base
%O A352942 1,8
%A A352942 _Michael S. Branicky_, May 11 2022