|
|
A095747
|
|
Maximally asymmetric odd primes in binary.
|
|
3
|
|
|
3, 5, 7, 11, 13, 19, 23, 29, 43, 53, 71, 79, 83, 101, 109, 113, 151, 179, 233, 241, 271, 311, 331, 347, 397, 421, 457, 599, 683, 739, 797, 853, 937, 977, 1087, 1103, 1223, 1307, 1427, 1459, 1597, 1613, 1733, 2017, 2111, 2143, 2503, 2731, 3011
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Primes p for which A037888(p) = floor((A070939(p)-2)/2). Those numbers contain just the first and last bits mirroring each other. Hence all the odd primes without leading zeros begin and end in 1 bits, the unique totally asymmetric prime being (10)_2 = 2.
|
|
LINKS
|
|
|
EXAMPLE
|
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.
|
|
PROG
|
(PARI)A070939(p)={return(floor(log(p)/log(2))+1)};
A037888(p)={v=binary(p); s=0; j=#v; for(k=1, #v, s+=abs(v[k]-v[j]); j--); return(s/2); }; forprime(p=3, 3011, if(A037888(p) ==floor((A070939(p)-2)/2), print1(p, ", ")))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|