A374402 - OEIS

%I #36 Aug 02 2024 12:07:43

%S 2,5,23,17,41,67,137,269,521,1049,2081,4111,8233,16417,32771,65537,

%T 131113,262147,524309,1048609,2097257,4194389,8388617,16777289,

%U 33554501,67109123,134217929,268435459,536871017,1073741827,2147484041,4294967497,8589934627,17179869731

%N Least number that is the lesser of two consecutive primes p and q whose binary expansions have the same length and agree at exactly n digit positions, or -1 if no such prime pair exists.

%e a(1) = 2 because 2 = 10_2 and 3 = 11_2 are two consecutive primes that, when written in base 2, both have 2 digits and agree at exactly 1 digit position (each has a 1 in its first digit position), and no earlier pair of consecutive primes has this property.

%e a(3) = 23 = 10111_2; the next prime is

%e        29 = 11101_2  (same number of binary digits),

%e             ^ ^ ^    and the digits agree at 3 digit positions,

%e   and no earlier pair of consecutive primes has this property.

%o (PARI) card(p)=my(u=binary(p),v=binary(nextprime(p+1))); if(#u!=#v,return(0)); sum(i=1,#u,u[i]==v[i])

%o a(n)=forprime(p=2^n,oo,if(card(p)==n,return(p)))

%Y Cf. A000040, A006879, A205510, A319840, A006879, A319840, A339080, A374176.

%K nonn,base

%O 1,1

%A _Jean-Marc Rebert_, Jul 07 2024