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%I #7 Oct 02 2015 13:06:17
%S 1,101,10103,10103011,10103011013,1010301101309,10103011013090003,
%T 101030110130900030009,10103011013090003000903,
%U 1010301101309000300090303,1010301101309000300090303009,1010301101309000300090303009059,1010301101309000300090303009059061
%N Minimal appendage-sequence of primes with seed 1, base 10, and appendages of the form 0s(n); see Comments.
%C The minimal appendage-sequence of primes with seed s and base b is defined as follows:
%C a(1) = s
%C a(2) = least prime that begins with s0;
%C a(3) = least prime that begins with a(2)0;
%C a(n) = least prime that begins with a(n-1)0.
%H Clark Kimberling, <a href="/A261965/b261965.txt">Table of n, a(n) for n = 1..300</a>
%e 11 comes from a(3) = 10103 by appending 011 to a(3); the result is the least prime that begins with 10103. Triangular format:
%e 1
%e 101
%e 10103
%e 10103011
%e 10103011013
%e 1010301101309
%e 10103011013090003
%e 101030110130900030009
%t base = 10; s = {{1}}; Do[NestWhile[# + 1 &, 1, (nn = #; ! PrimeQ[FromDigits[tmp=IntegerDigits[FromDigits[Flatten[IntegerDigits[Join[Last[s], {0}, IntegerDigits[nn - Sum[base^n, {n, l = NestWhile[# + 1 &, 1, ! (nn - (Sum[base^n, {n, #}]) < 0) &] - 1}], base, l + 1]]]]]], base]]) &]; AppendTo[s, {FromDigits[tmp]}], {20}];
%t Flatten[s] (* _Peter J. C. Moses_, Sep 03 2015 *)
%Y Cf. A261966.
%K nonn,easy,base
%O 1,2
%A _Clark Kimberling_, Sep 25 2015
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