1,1

A prime p is a base-b deletable prime if when written in base b it has the property that removing some digit leaves either the empty string or another deletable prime. However, in base 2 we adopt the convention that 2 = 10 and 3 = 11 are deletable.

Deleting a digit cannot leave any leading zeros in the new string. For example, deleting the 2 in 2003 to obtain 003 is not allowed.

Lei Zhou, Table of n, a(n) for n = 1..10000

isDel := proc(n::integer) local b2, redu, rpr, d; if n = 2 or n =3 then RETURN(true); elif not isprime(n) then RETURN(false); else b2 := convert(n, base, 2); for d from 1 to nops(b2) do redu := [op(1..d-1, b2), op(d+1..nops(b2), b2) ]; if op(nops(redu), redu) = 1 then rpr := sum( op(i, redu)*2^(i-1), i=1..nops(redu)); if isDel(rpr) then RETURN(true); fi; fi; od; RETURN(false); fi; end: for n from 1 to 200 do if isDel(ithprime(n)) then printf("%d, ", ithprime(n)); fi; od: # R. J. Mathar, Apr 25 2006

a = {}; c = {1}; While[Length[a] < 100, b = c; c = {}; lb = Length[b]; Do[nb = b[[ib]]; cdb = RealDigits[nb, 2]; db = cdb[[1]]; ldb = cdb[[2]]; Do[dc = Insert[db, 0, j]; nc = FromDigits[dc, 2]; If[PrimeQ[nc], AppendTo[c, nc]], {j, 2, ldb + 1}]; Do[dc = Insert[db, 1, j]; nc = FromDigits[dc, 2]; If[PrimeQ[nc], AppendTo[c, nc]], {j, 2, ldb + 1}], {ib, 1, lb}]; c = Union[{}, c]; a = Union[a, c]]; a (* Lei Zhou, Mar 06 2015 *)

a = {0, 2}; d = {2, 3};

For[n = 3, n <= 15, n++,

p = Select[Range[2^(n - 1), 2^n - 1], PrimeQ[#] &];

For[i = 1, i <= Length[p], i++,

c = IntegerDigits[p[[i]], 2];

For[j = 1, j <= n, j++,

t = Delete[c, j];

If[t[[1]] == 0, Continue[]];

If[MemberQ[d, FromDigits[t, 2]], AppendTo[d, p[[i]]]; Break[]]]]];

d (* Robert Price, Nov 11 2018 *)

(Python)

from sympy import isprime

def ok(n):

if not isprime(n): return False

if n == 2 or n == 3: return True

b = bin(n)[2:]

bi = (b[:i]+b[i+1:] for i in range(len(b)))

return any(t[0] != '0' and ok(int(t, 2)) for t in bi)

print([k for k in range(614) if ok(k)]) # Michael S. Branicky, Jan 13 2022

Cf. A080608, A080603, A096235-A096245.

Sequence in context: A049643 A005728 A050437 * A371694 A106639 A233462

Adjacent sequences: A096243 A096244 A096245 * A096247 A096248 A096249

nonn,base,easy

Michael Kleber, Feb 28 2003

More terms from R. J. Mathar, Apr 25 2006

approved