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A096246 Base-2 deletable primes (written in base 10). 27
2, 3, 5, 7, 11, 13, 19, 23, 29, 37, 43, 47, 53, 59, 61, 73, 79, 83, 101, 107, 109, 137, 149, 151, 157, 163, 167, 173, 179, 197, 211, 229, 277, 281, 293, 307, 311, 313, 317, 331, 347, 349, 359, 389, 397, 419, 421, 457, 461, 467, 557, 563, 569, 587, 599, 601, 613 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

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

MAPLE

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A080608, A080603, A096235-A096245.

Sequence in context: A049643 A005728 A050437 * A106639 A233462 A233893

Adjacent sequences:  A096243 A096244 A096245 * A096247 A096248 A096249

KEYWORD

nonn,base,easy

AUTHOR

Michael Kleber, Feb 28 2003

EXTENSIONS

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

STATUS

approved

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Last modified December 10 09:49 EST 2018. Contains 318047 sequences. (Running on oeis4.)