This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A328625 #22 Oct 25 2019 18:09:25
%S A328625 0,1,2,5,4,3,6,7,14,17,22,21,12,13,26,29,10,9,18,19,8,11,28,27,24,25,
%T A328625 20,23,16,15,30,31,32,35,34,33,66,67,74,77,82,81,102,103,116,119,100,
%U A328625 99,138,139,128,131,148,147,174,175,170,173,166,165,60,61,62,65,64,63,126,127,134,137,142,141,192,193,206,209,190,189,48,49,38,41,58,57,114
%N A328625 In primorial base representation of n, multiply all other digits except the least significant with 1+{their right hand side neighbor}, and reduce each modulo prime(k) (with k > 1) to get a new digit for the position k (the least significant digit stays as it is), then convert back to decimal.
%C A328625 In primorial base (see A049345) we keep the least significant digit (0 or 1) intact, and replace each digit d(i) left of that (for i >= 2) with a new digit value computed as d(i)*(1+d(i-1)) mod prime(i). a(n) is then the newly constructed primorial expansion converted back to decimal.
%C A328625 Because for all primes p, Z_p is a field (not just a ring), this sequence is a permutation of nonnegative integers, and roughly speaking, offers a kind of analog of A003188 for primorial base system. Note however that it is the digit neighbor on the right (not left) hand side that affects here what will be the new digit at each position.
%H A328625 Antti Karttunen, <a href="/A328625/b328625.txt">Table of n, a(n) for n = 0..30029</a>
%H A328625 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A328625 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328625 a(n) = A276085(A328624(n)).
%F A328625 For all n, A328620(a(n)) = A328620(n).
%e A328625 In primorial base (A049345) 199 is written as "6301" because 6*A002110(3) + 3*A002110(2) + 0*A002110(1) + 1*A002110(0) = 6*30 + 3*6 + 0*2 + 1*1 = 199. Multiplying each digit left of the least significant by 1+{digit one step right}, and reducing modulo the corresponding prime yields 4*6 mod 7, 1*3 mod 5, 2*0 mod 3, (with the least significant 1 staying the same), so we get "3301", which is the primorial base expansion of 109, thus a(199) = 109.
%o A328625 (PARI)
%o A328625 A002110(n) = prod(i=1,n,prime(i));
%o A328625 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A328625 A328624(n) = { my(m=1, p=2, e, g=1); while(n, e = (n%p); m *= (p^((g*e)%p)); g = e+1; n = n\p; p = nextprime(1+p)); (m); };
%o A328625 A328625(n) = A276085(A328624(n));
%Y A328625 Cf. A002110, A049345, A276085, A328620, A328624, A328626 (inverse permutation), A328628.
%Y A328625 Cf. also A003188, A289234, A328622.
%K A328625 nonn
%O A328625 0,3
%A A328625 _Antti Karttunen_, Oct 23 2019