OFFSET
1,1
COMMENTS
The terms of this sequence have necessarily an odd number >= 3 of digits.
There is only one term whose digits > 0 are all equal: 101.
The only cyclops primes (A134809) of this sequence are the first 15 terms from 101 to 907.
The first palindromes of this sequence are 101, 10301, 10501, 10601, 30103, 30203, 30403, 30703, 30803, ...
Intersection with A309101 = {503, 10103, 10303, 10903, ...}.
EXAMPLE
103 is the smallest term with two distinct digits > 0.
10607 is the smallest term with three distinct digits > 0.
MATHEMATICA
aQ[n_] := PrimeQ[n] && OddQ[(m = Length[(d = IntegerDigits[n])])] && Flatten@Position[d, _?(# == 0 &)] == Range[2, m, 2]; Select[Range[100, 31000], aQ] (* Amiram Eldar, Aug 04 2019 *)
PROG
(Magma) sol:=[]; m:=1; for p in PrimesInInterval(101, 50000) do v:=Reverse(Intseq(p)); test:=0; for u in [1..#v-1] do if u mod 2 eq 0 and v[u] eq 0 and v[u+1] ne 0 then test:=test+1; end if; end for; if test eq (#v-1)/2 then sol[m]:=p; m:=m+1; end if; end for; sol; // Marius A. Burtea, Aug 04 2019
(PARI) eva(n) = subst(Pol(n), x, 10)
f(n) = my(d=digits(n)); eva(vector(2*#d-1, k, if (k%2, d[1+k\2]))) \\ from Michel Marcus
terms(n) = my(i=0); for(k=10, oo, if(i>=n, break); if(vecmin(digits(k)) > 0, my(iz=f(k)); if(ispseudoprime(iz), print1(iz, ", "); i++)))
/* Print initial 40 terms as follows: */
terms(40) \\ Felix Fröhlich, Aug 08 2019
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Aug 04 2019
STATUS
approved