

A364142


Sophie Germain primes p such that both p and the corresponding safe prime 2*p+1 have distinct digits.


2



2, 3, 23, 29, 41, 53, 83, 89, 173, 179, 239, 251, 281, 293, 359, 419, 431, 491, 641, 653, 683, 719, 743, 761, 953, 1289, 1409, 1439, 1583, 1973, 2039, 2063, 2069, 2351, 2543, 2693, 2741, 2819, 2903, 2963, 3491, 3761, 3821, 4019, 4073, 4271, 4793, 4871, 5231, 6173, 6329, 6491, 6983, 7043, 7103
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OFFSET

1,1


COMMENTS

The last term is a(1514) = 493250861 and the corresponding safe prime is 2*493250861 + 1 = 986501723.
The bfile contains all 1514 terms.


LINKS



EXAMPLE

a(4) = 29 is a term because 29 and 2*29 + 1 = 59 are both primes and both have distinct digits.


MAPLE

filter:= proc(p) local L;
L:= convert(p, base, 10);
if nops(L) <> nops(convert(L, set)) or not isprime(2*p+1) then return false fi;
L:= convert(2*p+1, base, 10);
nops(L) = nops(convert(L, set))
end proc:
select(filter, [seq(ithprime(i), i=1..1000)]);


MATHEMATICA

s = {p = 2}; Do[p = NextPrime[p]; While[! PrimeQ[q = 2*p + 1]  1<
Max[DigitCount[q]]  1 < Max[DigitCount[p]], p = NextPrime[p]]; AppendTo[s,
p], {1515}]; s


CROSSREFS



KEYWORD

nonn,base,fini,full


AUTHOR



STATUS

approved



