A211972 Prime numbers which cannot become prime by removing any number of initial binary digits.

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

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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
\\ Charles R Greathouse IV, Feb 20 2013

Crossrefs

Cf. A004676, A007088-A007095, A196095.

Sequence in context: A270539 A053182 A348153 * A339855 A076706 A243441

Adjacent sequences: A211969 A211970 A211971 * A211973 A211974 A211975

Keyword

nonn,base

Author

Irina Gerasimova, Feb 13 2013

Status

approved