A354469 - OEIS

%I #6 Jun 05 2022 08:32:45

%S 0,1,4,5,2,3,24,25,28,29,26,27,18,19,22,23,20,21,12,13,16,17,14,15,6,

%T 7,10,11,8,9,180,181,184,185,182,183,204,205,208,209,206,207,198,199,

%U 202,203,200,201,192,193,196,197,194,195,186,187,190,191,188,189

%N Write n in primorial base, then replace each nonzero digit d of radix p with p-d.

%C This sequence is a self-inverse permutation of the nonnegative integers, similar to A225901.

%C There are exactly two fixed points: a(0) = 0 and a(1) = 1.

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e For n = 42:

%e - the primorial base expansion of 42 is: (1, 2, 0, 0),

%e - the corresponding radixes are: (7, 5, 3, 2),

%e - so the primorial base expansion of a(42) is: (7-1, 5-2, 0, 0) = (6, 3, 0, 0),

%e - and a(42) = 198.

%o (PARI) a(n, s=i->prime(i)) = { my (v=0, f=1, r); for (i=1, oo, if (n==0, return (v), r=s(i); v+=f*((-n)%r); f*=r; n\=r)) }

%Y Cf. A225901, A235168.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Jun 02 2022