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A374233 Irregular triangle read by rows where row n lists the primes containing at least one digit not seen in any smaller prime in base n, for n >= 2.

%I A374233 #45 Jul 06 2024 09:25:14
%S A374233 2,2,3,2,3,5,17,2,3,5,19,2,3,5,7,29,37,2,3,5,7,11,13,2,3,5,7,11,37,53,
%T A374233 67,2,3,5,7,11,13,17,59,83,2,3,5,7,11,19,41,61,83,101,2,3,5,7,11,17,
%U A374233 19,31,37,43,2,3,5,7,11,13,53,73,97,109,127,149
%N A374233 Irregular triangle read by rows where row n lists the primes containing at least one digit not seen in any smaller prime in base n, for n >= 2.
%e A374233 Row n=4 is 2, 3, 5, 17, which is 2_4, 3_4, 11_4, 101_4.
%e A374233 First few rows:
%e A374233        k=1  2  3   4   5   6   7   8
%e A374233   n=2:  [2],
%e A374233   n=3:  [2, 3],
%e A374233   n=4:  [2, 3, 5, 17],
%e A374233   n=5:  [2, 3, 5, 19],
%e A374233   n=6:  [2, 3, 5,  7, 29, 37],
%e A374233   n=7:  [2, 3, 5,  7, 11, 13],
%e A374233   n=8:  [2, 3, 5,  7, 11, 37, 53, 67],
%e A374233   ...
%o A374233 (Python)
%o A374233 from sympy.ntheory import digits, nextprime
%o A374233 def row(n):
%o A374233     if n == 2: return [2]
%o A374233     p, r, used = 2, [2], {2}
%o A374233     while len(used) < n:
%o A374233         while (ds:=set(digits(p:=nextprime(p), n)[1:])) <= used: pass
%o A374233         r.append(p)
%o A374233         used |= ds
%o A374233     return r
%o A374233 print([an for b in range(2, 13) for an in row(b)]) # _Michael S. Branicky_, Jul 01 2024
%o A374233 (PARI) isok(d, digs) = for (i=1, #d, if (!vecsearch(digs, d[i]), return(1)));
%o A374233 row(n) = my(digs=List(), v=List()); forprime(p=2, , my(d = digits(p, n)); if (isok(d, Vec(digs)), listput(v, p); for (i=1, #d, listput(digs, d[i])); listsort(digs, 1); if (#digs == n, return(Vec(v))););); \\ _Michel Marcus_, Jul 02 2024
%Y A374233 Cf. A033274.
%K A374233 base,easy,nonn,tabf
%O A374233 2,1
%A A374233 _Nicolas Bělohoubek_, Jul 01 2024