cp's OEIS Frontend

A374402 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.

%I A374402 #36 Aug 02 2024 12:07:43
%S A374402 2,5,23,17,41,67,137,269,521,1049,2081,4111,8233,16417,32771,65537,
%T A374402 131113,262147,524309,1048609,2097257,4194389,8388617,16777289,
%U A374402 33554501,67109123,134217929,268435459,536871017,1073741827,2147484041,4294967497,8589934627,17179869731
%N A374402 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 A374402 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 A374402 a(3) = 23 = 10111_2; the next prime is
%e A374402        29 = 11101_2  (same number of binary digits),
%e A374402             ^ ^ ^    and the digits agree at 3 digit positions,
%e A374402   and no earlier pair of consecutive primes has this property.
%o A374402 (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 A374402 a(n)=forprime(p=2^n,oo,if(card(p)==n,return(p)))
%Y A374402 Cf. A000040, A006879, A205510, A319840, A006879, A319840, A339080, A374176.
%K A374402 nonn,base
%O A374402 1,1
%A A374402 _Jean-Marc Rebert_, Jul 07 2024