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A262637
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Minimal nested palindromic base-4 primes with seed 2; see Comments.
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3
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2, 323, 3332333, 333323333, 33333233333, 103333323333301, 1210333332333330121, 100212103333323333301212001, 3310021210333332333330121200133, 3303310021210333332333330121200133033, 11330331002121033333233333012120013303311
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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) = 3332333 is the least base-4 prime having a(2) = 323 in its middle.
Triangular format:
2
323
3332333
333323333
33333233333
103333323333301
1210333332333330121
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MATHEMATICA
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s = {2}; 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 (* A262637 *)
Map[FromDigits[ToString[#], base] &, s] (* A262638 *)
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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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