A051846 Digits 1..n in strict descending order n..1 interpreted in base n+1.
1, 7, 57, 586, 7465, 114381, 2054353, 42374116, 987654321, 25678050355, 736867805641, 23136292864686, 789018236134297, 29043982525261081, 1147797409030816545, 48471109094902544776, 2178347851919531492065, 103805969587115219182431
Offset: 1
Examples
a(1) = 1, a(2) = 2*3 + 1 = 7, a(3) = 3*(4^2) + 2*4 + 1 = 57, a(4) = 4*(5^3) + 3*(5^2) + 2*5 + 1 = 586.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..200
- Chai Wah Wu, Pandigital and penholodigital numbers, arXiv:2403.20304 [math.GM], 2024. See p. 1.
Programs
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Maple
a(n) := proc(n) local i; add(i*((n+1)^(i-1)),i=1..n); end;
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Mathematica
Array[Sum[i*(# + 1)^(i - 1), {i, #}] &, 18] (* Michael De Vlieger, Apr 04 2024 *) -
Maxima
makelist(((n+1)^(n+1)*(n-1) + 1)/n^2,n,1,20); /* Martin Ettl, Jan 25 2013 */
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PARI
a(n)=((n+1)^(n+1)*(n-1)+1)/n^2
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Python
def a(n): return sum((i+1)*(n+1)**i for i in range(n)) print([a(n) for n in range(1, 20)]) # Michael S. Branicky, Apr 10 2022
Formula
a(n) = Sum_{i=1..n} i*(n+1)^(i-1).
a(n) = ((n+1)^(n+1)*(n-1) + 1)/n^2 = A062806(n+1)/(n+1) - (n+1)^(n+1). - Benoit Cloitre, Sep 28 2002
a(n) = (n-1) * A058128(n+1) + 1. - Seiichi Manyama, Apr 10 2022
Extensions
Minor edits in formulas by M. F. Hasler, Oct 11 2019
Comments