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Minimal prime concatenation sequence with base 2 and seed 11.
3

%I #13 Sep 25 2020 07:13:38

%S 11,111,11101,111011,11101111,111011111,111011111001,111011111001111,

%T 1110111110011111,11101111100111110101,1110111110011111010101,

%U 11101111100111110101010101,11101111100111110101010101011,1110111110011111010101010101111

%N Minimal prime concatenation sequence with base 2 and seed 11.

%H Clark Kimberling, <a href="/A261269/b261269.txt">Table of n, a(n) for n = 1..500</a>

%e 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 11

%e 111

%e 11101

%e 111011

%e 11101111

%e 1110111111

%e 111011111001

%t b = 2; s = {{1}};

%t 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 AppendTo[s, tmp], {30}]; Map[FromDigits, s]

%t Map[FromDigits, s] (* A261269 *)

%t Map[FromDigits[#, b] &, s] (* A261270 *)

%t (* _Peter J. C. Moses_, Aug 06 2015 *)

%Y Cf. A261270.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Sep 16 2015