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A212223
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a(n) is the least integer greater than 1 whose expansion in prime bases 2 to prime(n) have equal sum of digits.
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2
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OFFSET
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1,1
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COMMENTS
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Case a(1) is trivial since only base prime(1)=2 is involved.
Conjecture: the sequence never terminates.
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LINKS
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EXAMPLE
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a(5) = 1386 because that number has the same sum of digits in the first 5 prime bases 2, 3, 5, 7, 11 (see A212222 and A000040).
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MATHEMATICA
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f[n_] := Block[{p = Prime@ Range@ n, k = 2}, While[ Length[ Union[ Total@# & /@ IntegerDigits[k, p]]] != 1, k++]; k] (* Robert G. Wilson v, Oct 24 2014 *)
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PROG
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(PARI) isok(n, k) = my(s=hammingweight(k)); forprime (b=3, prime(n), if (sumdigits(k, b) != s, return (0))); return (1);
a(n) = my(k=2); while (!isok(n, k), k++); k; \\ Michel Marcus, Jun 08 2021
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CROSSREFS
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KEYWORD
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nonn,base,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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