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URL: https://oeis.org/A107367

⇱ A107367 - OEIS

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A107367
Primes whose digits do not appear in three previous terms.
1
2, 3, 5, 7, 11, 23, 59, 67, 101, 223, 449, 557, 601, 823, 4999, 5557, 6011, 8233, 9949, 57557, 60101, 82223, 94949, 555557, 600011, 822223, 994949, 5555777, 6000011, 8222323, 9444949, 55555777, 60000011, 82223233, 94449449, 555557557, 600000001, 822222223, 944444999
OFFSET
1,1
COMMENTS
From Michael S. Branicky, Jan 02 2026: (Start)
Terms must be increasing. If not unique, then 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, ... works. If unique, but not increasing, then sequence starts 2, 3, 5, 7, 11, 23, 59, 47, 61, 83, ... .
a(4004) has 1001 digits. (End)
LINKS
Michael S. Branicky, Python program for OEIS A107367
MATHEMATICA
d=2; e=3; f=5; b={2, 3, 5}; id[t_]:=IntegerDigits[t]; Do[p=Prime[n]; If[Intersection[Union[id[d], id[e], id[f]], id[p]]=={}, b=Append[b, p]; d=e; e=f; f=p], {n, 100000}]; b
nxt[{a_, b_, c_}]:=Module[{dgs=Union[Flatten[IntegerDigits/@{a, b, c}]], d = NextPrime[ c]}, While[ Intersection[dgs, IntegerDigits[d]]!={}, d= NextPrime[d]]; {b, c, d}]; NestList[nxt, {2, 3, 5}, 30][[All, 1]] (* Harvey P. Dale, Oct 11 2021 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Zak Seidov, May 24 2005
EXTENSIONS
More terms from Harvey P. Dale, Oct 11 2021
a(32) onward from Michael S. Branicky, Jan 01 2026
STATUS
approved