A261200 - OEIS

%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