A061247 Prime numbers with every digit a perfect cube, i.e., consisting of only digits 0, 1 and 8.

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

Robert Israel, Table of n, a(n) for n = 1..17482

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

Cf. A061246, A020449-A020472, A199325-A199329.

Sequence in context: A084987 A083185 A007597 * A199328 A370447 A068188

Adjacent sequences: A061244 A061245 A061246 * A061248 A061249 A061250

Keyword

nonn,base,less

Author

Amarnath Murthy, Apr 23 2001

Extensions

Corrected and extended by Stefan Steinerberger, Jun 10 2007

Status

approved