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A080608
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Deletable primes: primes such that removing some digit leaves either the empty string or another deletable prime.
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43
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2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 103, 107, 113, 127, 131, 137, 139, 157, 163, 167, 173, 179, 193, 197, 223, 229, 233, 239, 263, 269, 271, 283, 293, 307, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 397, 431, 433, 439
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OFFSET
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1,1
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COMMENTS
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Subsequence of A179336. - Reinhard Zumkeller, Jul 11 2010
Leading zeros are allowed, for example the prime 100003 is deletable because of the sequence 00003, 0003, 003, 03, 3 consists of primes. Because of this, it appears that deletable primes are relatively common in the region just above a power of ten. For example 10^1000 + 2713 is a deletable prime. - Jeppe Stig Nielsen, Aug 01 2018
For a version that does not allow leading zeros, see A305352. - Jeppe Stig Nielsen, Aug 01 2018
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LINKS
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David W. Wilson, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Deletable Prime
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EXAMPLE
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410256793 is a deletable prime since each member of the sequence 410256793, 41256793, 4125673, 415673, 45673, 4567, 467, 67, 7 is prime (Weisstein, Caldwell).
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MAPLE
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read("transforms"):
isA080608 := proc(n)
option remember;
local dgs, i ;
if isprime(n) then
if n < 10 then
true;
else
dgs := convert(n, base, 10) ;
for i from 1 to nops(dgs) do
subsop(i=NULL, dgs) ;
digcatL(ListTools[Reverse](%)) ;
if procname(%) then
return true;
end if;
end do:
false ;
end if;
else
false;
end if;
end proc:
n := 1;
for i from 1 to 500 do
p := ithprime(i) ;
if isA080608(p) then
printf("%d %d\n", n, p) ;
n := n+1 ;
fi ;
end do: # R. J. Mathar, Oct 11 2014
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MATHEMATICA
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Rest@ Union@ Nest[Function[{a, p}, Append[a, With[{w = IntegerDigits[p]}, If[# == True, p, 0] &@ AnyTrue[Array[FromDigits@ Delete[w, #] &, Length@ w], ! FreeQ[a, #] &]]]] @@ {#, Prime[Length@ # + 1]} &, Prime@ Range@ PrimePi@ 10, 81] (* Michael De Vlieger, Aug 02 2018 *)
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PROG
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(PARI) is(n) = !ispseudoprime(n)&&return(0); my(d=digits(n)); #d==1&&return(1); for(i=1, #d, is(fromdigits(vecextract(d, Str("^"i))))&&return(1)); 0 \\ Jeppe Stig Nielsen, Aug 01 2018
(Perl) use ntheory ":all"; sub is { my $n=shift; return 0 unless is_prime($n); my @d=todigits($n); return 1 if @d==1; is(fromdigits([vecextract(\@d, ~(1<<$_))])) && return 1 for 0..$#d; 0; } # Dana Jacobsen, Nov 16 2018
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CROSSREFS
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Cf. A080603, A096235-A096246, A305352.
Sequence in context: A247980 A234851 A179336 * A305352 A137812 A216578
Adjacent sequences: A080605 A080606 A080607 * A080609 A080610 A080611
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KEYWORD
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nonn,easy,base
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AUTHOR
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David W. Wilson, Feb 25 2003
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STATUS
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approved
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