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A096246
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Base-2 deletable primes (written in base 10).
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15
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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; internal format)
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OFFSET
| 1,1
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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.
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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 (mathar(AT)strw.leidenuniv.nl), Apr 25 2006
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CROSSREFS
| Cf. A080608, A080603, A096235-A096245.
Sequence in context: A005728 A049643 A050437 * A106639 A078334 A108696
Adjacent sequences: A096243 A096244 A096245 * A096247 A096248 A096249
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KEYWORD
| nonn,base
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AUTHOR
| Michael Kleber (michael.kleber(AT)gmail.com), Feb 28 2003
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 25 2006
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