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A306085
Primes which have an even decimal digit and remain prime after all even digits are removed.
3
23, 43, 47, 67, 83, 101, 103, 107, 109, 127, 149, 163, 167, 181, 211, 223, 227, 263, 271, 283, 307, 347, 367, 419, 431, 443, 463, 467, 479, 487, 503, 509, 523, 563, 569, 607, 613, 617, 619, 631, 643, 647, 653, 659, 673, 683, 701, 709, 743, 761, 769, 811, 823, 827, 853, 859, 863, 883, 887, 907
OFFSET
1,1
COMMENTS
A proper subset of A306084.
LINKS
EXAMPLE
101 is a member of the sequence because it has an even digit, 0, and with its removal, the resulting number 11 is a prime.
MAPLE
filter:= proc(n) local L, Lp;
if not isprime(n) then return false fi;
L:= convert(n, base, 10);
Lp:= subs([0=NULL, 2=NULL, 4=NULL, 6=NULL, 8=NULL], L);
if L = Lp then return false fi;
isprime(add(Lp[i]*10^(i-1), i=1..nops(Lp)))
end proc:
select(filter, [seq(n, n=11..1000, 2)]); # Robert Israel, Jul 04 2018
MATHEMATICA
fQ[n_] := Block[{id = IntegerDigits@ n}, Select[id, EvenQ] != {} && PrimeQ[ FromDigits[ Select[id, OddQ]] ]]; Select[Prime@ Range@ 160, fQ]
PROG
(PARI) isok(p) = isprime(p) && (d=digits(p)) && #select(x->!(x%2), d) && isprime(fromdigits(select(x->(x % 2), d))); \\ Michel Marcus, Jun 22 2018
CROSSREFS
Sequence in context: A304390 A309533 A331342 * A037137 A340136 A154530
KEYWORD
nonn,base
AUTHOR
STATUS
approved