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A061247
Prime numbers with every digit a perfect cube, i.e., consisting of only digits 0, 1 and 8.
11
11, 101, 181, 811, 881, 1181, 1801, 1811, 8011, 8081, 8101, 8111, 10111, 10181, 11801, 18181, 80111, 81001, 81101, 81181, 88001, 88801, 88811, 100801, 100811, 101081, 101111, 108011, 108881, 110881, 118081, 118801, 180001, 180181, 180811
OFFSET
1,1
COMMENTS
The intersection with A007500 is listed in A199328. - M. F. Hasler, Nov 05 2011
LINKS
EXAMPLE
a(6) = 1801, 1801 is a prime and consists of only 1, 8 and 0.
MAPLE
N:= 1000: # to get the first N entries
count:= 0:
allowed:= {0, 1, 8}:
nallowed:= nops(allowed):
subst:= seq(i=allowed[i+1], i=0..nallowed-1);
for d from 1 while count < N do
for x1 from 1 to nallowed-1 while count < N do
for t from 0 to nallowed^d-1 while count < N do
L:= subs(subst, convert(x1*nallowed^d+t, base, nallowed));
X:= add(L[i]*10^(i-1), i=1..d+1);
if isprime(X) then
count:= count+1;
A[count]:= X;
fi
od od od:
seq(A[n], n=1..N); # Robert Israel, Apr 20 2014
MATHEMATICA
Select[Prime[Range[50000]], Length[Union[{0, 1, 8}, IntegerDigits[ # ]]] == 3&] (* Stefan Steinerberger, Jun 10 2007 *)
Select[FromDigits/@Tuples[{0, 1, 8}, 6], PrimeQ] (* Harvey P. Dale, Jan 12 2016 *)
PROG
(PARI) a(n=50, L=[0, 1, 8], show=0)={my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1 && !L[1]), #L]), ispseudoprime(t=vector(d, i, L[v[i]])*u) || next; show && print1(t", "); n-- || return(t)))} \\ M. F. Hasler, Nov 05 2011
(Magma) [NthPrime(n): n in [1..2*10^4] | forall{d: d in Intseq(NthPrime(n)) | d in [0, 1, 8]}]; // Vincenzo Librandi, May 15 2019
CROSSREFS
KEYWORD
nonn,base,less
AUTHOR
Amarnath Murthy, Apr 23 2001
EXTENSIONS
Corrected and extended by Stefan Steinerberger, Jun 10 2007
STATUS
approved