A095758 Number of A095748-primes in range ]2^n,2^(n+1)].
0, 0, 0, 2, 5, 4, 4, 15, 16, 24, 33, 56, 72, 95, 149, 219, 322, 537, 655, 998, 1309, 1859, 2784, 3886, 5340, 8091, 10718, 16191, 22316, 30372, 43425, 63699, 88186
Offset: 1
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.
a(1) = A(1,1) = 3 (11 in binary) as it is the first prime whose binary expansion is palindromic. a(2) = A(1,2) = 5 (101 in binary) as it is the second prime whose binexp is palindromic. a(3) = A(2,1) = 2 (10 in binary) as it is the first prime whose binexp needs a flip of just one bit to become palindrome. a(4) = A(1,3) = 7 (111 in binary) as it is the third prime whose binexp is palindromic. a(5) = A(2,2) = 11 (1011 in binary) as it is the second prime whose binexp needs a flip of just one bit to become palindrome.
f:= proc(n) local L,i; L:= convert(n,base,2); add(abs(L[i]-L[-i]),i=1..floor(nops(L)/2)) end proc: select(t -> f(t) = 1, [seq(ithprime(i),i=1..1000)]); # Robert Israel, Dec 04 2023
a(10)=(110101)2 since the symmetry is limited to the first and last bits. The number 47=(101111)2 is not a term because from left to right, the third bit matches with the fourth.
Comments