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 A096246 Base-2 deletable primes (written in base 10). 37
 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 *) PROG (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 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 July 4 08:01 EDT 2022. Contains 355070 sequences. (Running on oeis4.)