A390511 - OEIS

%I #17 Jan 18 2026 23:45:37

%S 7,31,151,1753,1747,1741,19471,118801,148537,148531,406951,2339089,

%T 2339041,51662599,51662593,73451737,232301497,450988159,1444257721,

%U 1444257709,1444257673,24061965049,24061965043,43553959723,43553959717,502429570231,1552841185993

%N a(n) = prime(A391807(n)).

%t t = Table[Mod[Prime[nn], 3], {nn, 10^8}];  (* A039701 *)

%t u = Map[SequencePosition[t, Flatten[Join[{ConstantArray[1, #], 2}]], 1] &, Range[21]]

%t Prime[Table[First[Flatten[u[[n]]]], {n, 1, 21}]]

%t (* _Peter J. C. Moses_, Dec 11 2025 *)

%o (Python)

%o from sympy import nextprime, prime

%o from itertools import count, islice

%o def agen(NN=10000): # generator of terms for n <= NN

%o     n, pk, residues = 1, 1, "X"*NN

%o     for k in count(1):

%o         pk = nextprime(pk)

%o         resk = pk%3

%o         if resk == 2:

%o             while residues.endswith("1"*n) and n <= NN:

%o                 yield prime(k-n)

%o                 n += 1

%o         residues = residues[1:] + str(resk)

%o print(list(islice(agen(), 13))) # _Michael S. Branicky_, Jan 11 2026

%Y Cf. A000040, A391796, A391807.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 05 2026

%E a(22)-a(25) from _Michael S. Branicky_, Jan 11 2026

%E a(26)-a(27) from _Jinyuan Wang_, Jan 16 2026