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A261966
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Minimal appendage-sequence of primes with seed 1, base 2, and appendages of the form 0s(n); see Comments.
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2
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1, 101, 101001, 101001011, 1010010110001, 1010010110001011, 101001011000101100101, 10100101100010110010100101, 101001011000101100101001010001, 101001011000101100101001010001000011, 10100101100010110010100101000100001101111
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OFFSET
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1,2
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COMMENTS
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The minimal appendage-sequence of primes with seed s and base b is defined as follows:
a(1) = s
a(2) = least prime that begins with s0;
a(3) = least prime that begins with a(2)0;
a(n) = least prime that begins with a(n-1)0.
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LINKS
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EXAMPLE
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a(7) = 101001011000101100101 comes from a(6) = 1010010110001011 by appending 00101 to a(6); the result is the least prime that begins with 1010010110001011. Note that "internal 0's" are possible; e.g., the appendage, 00101 in a(6) contains an "internal 0" (the 3rd 0). Triangular format:
1
101
101001
101001011
1010010110001
1010010110001011
101001011000101100101
10100101100010110010100101
101001011000101100101001010001
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MATHEMATICA
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base = 2; 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]}], {12}];
u = Flatten[s]
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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