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A072807
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n-th prime prime(n) written in base (prime(n) (mod prime(n-1))).
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5
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111, 101, 111, 23, 1101, 101, 10011, 113, 45, 11111, 101, 221, 101011, 233, 125, 135, 111101, 151, 1013, 1001001, 211, 1103, 225, 141, 1211, 1100111, 1223, 1101101, 1301, 91, 2003, 345, 10001011, 149, 10010111, 421, 431, 2213, 445, 455, 10110101
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OFFSET
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2,1
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LINKS
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EXAMPLE
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Eventually non-decimal digit symbols appear, as in case of 307=17d, in base 14 = 307 mod 293.
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MAPLE
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a:= proc(n) local b, p, l;
p:= ithprime(n); b:= irem(p, prevprime(p));
if b=1 then l:= 1$p
else l:= ""; while p>0 do l:= irem(p, b, 'p'), l od
fi; parse(cat(l))
end:
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MATHEMATICA
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Table[BaseForm[Prime[w], Mod[Prime[w], Prime[w-1]]], {w, 2, 128}]
Join[{111}, FromDigits[IntegerDigits[#[[2]], Mod[#[[2]], #[[1]]]]]&/@ Partition[ Prime[Range[2, 50]], 2, 1]] (* Harvey P. Dale, Jul 03 2021 *)
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PROG
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(PARI) a(n) = {my(p=prime(n), q=prime(n-1)); if ((p % q) != 1, d=digits(p, p % q); if (#select(x->(x>9), d), 0, fromdigits(d, 10)), fromdigits(vector(p, k, 1), 10)); } \\ Michel Marcus, Sep 05 2019
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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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EXTENSIONS
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STATUS
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approved
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