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A262643
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Minimal nested palindromic base-5 primes with seed 3; see Comments.
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3
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3, 131, 31313, 1313131, 413131314, 2341313131432, 40234131313143204, 144023413131314320441, 2314402341313131432044132, 2202314402341313131432044132022, 14220231440234131313143204413202241, 20114220231440234131313143204413202241102
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OFFSET
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1,1
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COMMENTS
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Using only base-5 digits 0,1,2,3,4, 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-5 primes with seed s.
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LINKS
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EXAMPLE
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a(3) = 31313 is the least base-5 prime having a(2) = 131 in its middle.
Triangular format:
3
131
31313
1313131
413131314
2341313131432
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MATHEMATICA
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s = {3}; base = 5; 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 (* A262643 *)
Map[FromDigits[ToString[#], base] &, s] (* A262644 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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