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A262639
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Minimal nested palindromic base-4 primes with seed 3; see Comments.
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4
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3, 131, 11311, 121131121, 1212113112121, 312121131121213, 101312121131121213101, 11131013121211311212131013111, 31311131013121211311212131013111313, 1011313111310131212113112121310131113131101, 310113131113101312121131121213101311131311013
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OFFSET
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1,1
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COMMENTS
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Using only base-4 digits 0,1,2,3, let s be a palindrome and put a(1) = s. Let a(2) be the least palindromic prime having s in the middle; for n > 2, let a(n) be the least palindromic prime have a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic base-4 primes with seed s.
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LINKS
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EXAMPLE
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a(3) = 11311 is the least base-4 prime having a(2) = 131 in its middle.
Triangular format:
3
131
11311
121131121
1212113112121
312121131121213
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MATHEMATICA
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s = {3}; base = 4; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s (* A262639 *)
Map[FromDigits[ToString[#], base] &, s] (* A262640 *)
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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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