A107814 a(1) = prime(14), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).

43, 3, 13, 11, 17, 7, 37, 23, 2, 29, 19, 31, 41, 47, 67, 61, 71, 73, 53, 5, 59, 79, 89, 83, 103, 101, 107, 97, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277

Offset: 1

Author

Zak Seidov and Eric Angelini, May 24 2005

Keywords

• nonn
• base

Comments

a(n) = prime(n) for almost all n. Probably a(n) = prime(n) for all n > N for some N, but N must be very large. - Charles R Greathouse IV, Jul 20 2011

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A107353.

Other cases of seed: A107801 (a(1) = 2), A107802 (a(1) = 3), A107803 (a(1) = 5), A107804 (a(1) = 7), A107805 (a(1) = 11), A107806 (a(1) = 13), A107807 (a(1) = 17), A107808 (a(1) = 19), A107809 (a(1) = 23), A107810 (a(1) = 29), A107811 (a(1) = 31), A107812 (a(1) = 37), A107813 (a(1) = 41).

Programs

Maple

Cands:= subsop(14=NULL, [seq(ithprime(i),i=1..1000)]):
S:= map(t -> convert(convert(t,base,10),set), Cands):
R:= 43: x:= 43: xs:= {3,4}:
for n from 2 to 100 do
  found:= false;
  for i from 1 do
    if S[i] intersect xs <> {} then
      R:= R, Cands[i];
      x:= Cands[i];
      xs:= S[i];
      Cands:= subsop(i=NULL,Cands);
      S:= subsop(i=NULL,S);
      found:= true;
      break
    fi
  od;
  if not found then break fi;
od:
R; # Robert Israel, Dec 16 2024

Mathematica

p=Prime[14];b={p};d=p;Do[Do[r=Prime[c];If[FreeQ[b, r]&&Intersection@@IntegerDigits/@{d, r}=!={}, b=Append[b, r];d=r;Break[]], {c, 1000}], {k, 60}];b

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Jul 20 2011