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%I #12 Sep 25 2020 07:15:08
%S 1,10,101,1011,10111,101111,10111111,101111111,101111111011,
%T 10111111101101,101111111011010011,10111111101101001101111,
%U 10111111101101001101111101,1011111110110100110111110101,101111111011010011011111010111,1011111110110100110111110101111
%N Minimal prime concatenation sequence with base 2 and seed 1.
%H Clark Kimberling, <a href="/A261200/b261200.txt">Table of n, a(n) for n = 1..500</a>
%e In base 2, the least prime starting with seed 1 is 10; the least prime starting with 10 is 101; the least prime starting with 101 is 1011. Triangular format:
%e 1
%e 10
%e 101
%e 1011
%e 10111
%e 101111
%e 10111111
%e 101111111
%e 101111111011
%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] (* A261200 *)
%t Map[FromDigits[#, b] &, s] (* A261201 *)
%t (* _Peter J. C. Moses_, Aug 06 2015 *)
%Y A055011, A261200 and A261201 are all essentially the same sequence.
%K nonn,easy,base
%O 1,2
%A _Clark Kimberling_, Sep 16 2015
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