|
|
A211972
|
|
Prime numbers which cannot become prime by removing any number of initial binary digits.
|
|
2
|
|
|
2, 3, 5, 17, 41, 73, 89, 97, 137, 193, 257, 281, 313, 409, 521, 569, 577, 641, 673, 761, 929, 953, 1033, 1049, 1153, 1289, 1409, 1657, 1721, 1801, 1913, 2081, 2113, 2297, 2593, 2713, 3137, 3257, 3361, 3449, 3617, 4129, 4153, 4217, 4481, 4513, 4729, 4793, 4993, 5113, 5153
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
In binary: 10, 11, 101, 10001, 101001, 1001001, 1011001, 1100001, 10001001, 11000001, 100000001, 100011001, 100111001, 110011001, 1000001001, 1000111001, 1001000001, 1010000001, ....
Smallest k > 1 such that n written in base k that cannot become prime (written in base k) by chopping off any of the initial consecutive digits: 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 5, 2, 3, 5, 3, 2, 2, 3, 3, 2, 5, 3, 11, 2, 2, 5, 3, 2, 5, 6, 3, 2, 2, 5, 5, 2, 3, 8, 5, 2, 2, 3, 7,...
|
|
LINKS
|
|
|
EXAMPLE
|
89 = 1011001_2 qualifies because none of 11001_2, 1001_2, and 1_2 are prime.
|
|
MATHEMATICA
|
cbpQ[n_]:=NoneTrue[FromDigits[#, 2]&/@With[{id=Rest[IntegerDigits[n, 2]]}, NestList[Rest[#]&, id, Length[id]-1]], PrimeQ]; Select[Prime[Range[700]], cbpQ] (* Harvey P. Dale, Jul 29 2024 *)
|
|
PROG
|
(PARI) A053644(n)=my(k=1); while(k<=n, k<<=1); k>>1
is(n)=isprime(n)&&while(n-=A053644(n), if(isprime(n), return(0))); 1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|