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 A325722 #46 Mar 03 2024 16:27:53 %S A325722 1,1,2,2,4,4,8,8,16,3,6,3,12,6,4,6,18,12,24,5,24,6,8,10,16,5,12,20,30, %T A325722 32,7,0,8,36,10,9,14,16,0,9,0,12,18,7,0,40,15,42,10,0,9,11,24,12,48,0, %U A325722 18,0,13,20,14,48,14,0,28,0,15,15,32,22,16,0,0,27,17,18,24,36,19,26,40,56,0,20,64,0,21,18,28,0,22,44,48,72 %N A325722 Start the sequence with a(1) = 1 and read the digits one by one from there. The sequence is always extended with the product d*k, d being the digit read and k the number of d digits present up to the point of the d digit taken. %C A325722 Every prime number > 7 appears only once and in natural order. - _Davide Rotondo_, Feb 08 2024 %H A325722 Carole Dubois, <a href="/A325722/b325722.txt">Table of n, a(n) for n = 1..5001</a> %H A325722 Carole Dubois, <a href="/A325722/a325722_1.png">Digit-count for this sequence and two others visible in the Xref section</a> %e A325722 The sequence starts with a(1) = 1. %e A325722 We read this 1, see that there is only one digit 1 so far in the sequence, thus k = 1; we have then d*k = 1 and this 1 becomes a(2); %e A325722 We read a(2) = 1, see that this 1 is the 2nd digit 1 so far in the sequence, thus k = 2; we have then d*k = 2 and this 2 becomes a(3); %e A325722 We read a(3) = 2, see that there is only one digit 2 so far in the sequence, thus k = 1; we have then d*k = 2 and this 2 becomes a(4); %e A325722 We read a(4) = 2, see that this 2 is the 2nd digit 2 so far in the sequence, thus k = 2; we have then d*k = 4 and this 4 becomes a(5); %e A325722 ... %e A325722 We read now the first digit of a(9) = 16 and see that this 1 is the 3rd digit 1 so far in the sequence, thus k = 3; we have then d*k = 3 and this 3 becomes a(10); %e A325722 We read now the second digit of a(9) = 16 and see that this 6 is the 1st digit 6 so far in the sequence, thus k = 1; we have then d*k = 6 and this 6 becomes a(11); etc. %e A325722 From _Kevin Ryde_, Feb 10 2024: (Start) %e A325722 Digits d from the sequence terms, their respective occurrence number k, and consequent terms a(n) = d*k, begin: %e A325722 d = 1 1 2 2 4 4 8 8 1 6 3 6 3 1 2 6 4 ... %e A325722 k = 1 2 1 2 1 2 1 2 3 1 1 2 2 4 3 3 3 ... %e A325722 d*k = 1 2 2 4 4 8 8 16 3 6 3 12 6 4 6 18 12 ... %e A325722 (End) %o A325722 (PARI) digs(x) = if (x, digits(x), [0]); %o A325722 countd(listd, posd, y) = my(nb=0); for (k=1, posd, if (listd[k] == y, nb++);); nb; %o A325722 lista(nn) = my(list=List(1), listd=List(1), pos=1, posd=1); for (n=1, nn, my(d = digs(list[pos])); for (i=1, #d, my(y = d[i], nb = countd(listd, posd, y)); listput(list, y*nb); my(dd = digs(y*nb)); for (j=1, #dd, listput(listd, dd[j]);); posd++;); pos++;); Vec(list); \\ _Michel Marcus_, Feb 09 2024 %Y A325722 Cf. A325721 where the same idea is developed, but with d+k instead of d*k. See also A308232 for the concatenation kd. %Y A325722 Cf. A322182. %K A325722 base,nonn %O A325722 1,3 %A A325722 _Eric Angelini_ and _Carole Dubois_, May 16 2019