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A351576
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Factorial base expansion of n reinterpreted as a primorial base expansion, then converted back to decimal.
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9
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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n = 313 has factorial base representation (see A007623) "23001" because 2*5! + 3*4! + 1*1! = 240+72+1 = 313. When this is reinterpreted as a primorial base expansion (see A049345), we obtain 2*A002110(4) + 3*A002110(3) + 1*A002110(0) = 511, therefore a(313) = 511.
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MATHEMATICA
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a[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; FromDigits[Reverse[s], MixedRadix[Reverse@ Prime@ Range@ Length[s]]]]; Array[a, 100, 0] (* Amiram Eldar, Feb 07 2024 *)
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PROG
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(PARI)
A002110(n) = prod(i=1, n, prime(i));
A276076(n) = { my(i=0, m=1, f=1, nextf); while((n>0), i=i+1; nextf = (i+1)*f; if((n%nextf), m*=(prime(i)^((n%nextf)/f)); n-=(n%nextf)); f=nextf); m; };
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
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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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