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A261269 Minimal prime concatenation sequence with base 2 and seed 11.

%I A261269 #13 Sep 25 2020 07:13:38
%S A261269 11,111,11101,111011,11101111,111011111,111011111001,111011111001111,
%T A261269 1110111110011111,11101111100111110101,1110111110011111010101,
%U A261269 11101111100111110101010101,11101111100111110101010101011,1110111110011111010101010101111
%N A261269 Minimal prime concatenation sequence with base 2 and seed 11.
%H A261269 Clark Kimberling, <a href="/A261269/b261269.txt">Table of n, a(n) for n = 1..500</a>
%e A261269 In base 2, the least prime starting with seed 1 is 11; the least prime starting with 11 is 111; the least prime starting with 111 is 11101. Triangular format:
%e A261269 11
%e A261269 111
%e A261269 11101
%e A261269 111011
%e A261269 11101111
%e A261269 1110111111
%e A261269 111011111001
%t A261269 b = 2; s = {{1}};
%t A261269 Do[NestWhile[# + 1 &, 0, ! (PrimeQ[FromDigits[tmp = Join[Last[s], (nn = #;           IntegerDigits[nn - Sum[b^n, {n, l = NestWhile[# + 1 &, 1, ! (nn - (Sum[b^n, {n, #}]) < 0) &] - 1}], b, l + 1])], b]]) &];
%t A261269 AppendTo[s, tmp], {30}]; Map[FromDigits, s]
%t A261269 Map[FromDigits, s] (* A261269 *)
%t A261269 Map[FromDigits[#, b] &, s] (* A261270 *)
%t A261269 (* _Peter J. C. Moses_, Aug 06 2015 *)
%Y A261269 Cf. A261270.
%K A261269 nonn,easy,base
%O A261269 1,1
%A A261269 _Clark Kimberling_, Sep 16 2015