A107367 - OEIS

A107367

Primes whose digits do not appear in three previous terms.

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

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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, Table of n, a(n) for n = 1..4003

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

Cf. A030284, A107798, A107799.

Sequence in context: A107798 A119660 A079148 * A373044 A378774 A036342

Adjacent sequences: A107364 A107365 A107366 * A107368 A107369 A107370

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