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A330129 a(n) is the last term of the analogous sequence to A121805, but with initial term n, or -1 if that sequence is infinite.

%I A330129 #31 Feb 07 2024 13:21:43
%S A330129 99999945,9999999999999918,36,9999945,999945,9999999999999999936,936,
%T A330129 9999999999972,999999936,999936,999936,99999945,999954,999918,72,
%U A330129 99999918,999999999927,18,999981,999999999999999963,99981,999999999999999963,999936,9999999999999918,9963
%N A330129 a(n) is the last term of the analogous sequence to A121805, but with initial term n, or -1 if that sequence is infinite.
%C A330129 The numbers of terms of the corresponding sequences are in A330128.
%H A330129 Michael S. Branicky, <a href="/A330129/b330129.txt">Table of n, a(n) for n = 1..10000</a>
%H A330129 Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, <a href="http://arxiv.org/abs/2401.14346">arXiv:2401.14346</a>, <a href="https://www.youtube.com/watch?v=_EHAdf6izPI">Youtube</a>
%t A330129 nxt[x_] := Block[{p=1, n=x}, While[n >= 10, n = Floor[n/10]; p *= 10]; p (n + 1)]; a[n_] := Block[{nT=1, nX=n, w1, w2, w3, x, it, stp, oX}, stp = 100; w1 = w2 = w3 = 0; While[True, oX = nX; nT++; x = 10*Mod[oX, 10]; nX = SelectFirst[Range[9], IntegerDigits[oX + x + #][[1]] == # &, 0]; If[nX == 0, Break[], nX = nX + oX + x]; If[nT == stp, stp += 100; w1=w2; w2=w3; w3=nX; If[w3 + w1 == 2 w2 && Mod[w3 - w2, 100] == 0, it = Floor[(nxt[nX] - nX - 1)/(w3 - w2)]; nT += it*100; nX += (w3 - w2)*it; w3=nX; stp += it*100]]]; oX]; Array[a, 30]
%o A330129 (Python)
%o A330129 def nxt(x):
%o A330129     p, n = 1, x
%o A330129     while n >= 10:
%o A330129         n //= 10
%o A330129         p *= 10
%o A330129     return p * (n + 1)
%o A330129 def a(n):
%o A330129     nT, nX, w1, w2, w3, stp  = 1, n, 0, 0, 0, 100
%o A330129     while True:
%o A330129         oX = nX
%o A330129         nT += 1
%o A330129         x = 10*(oX%10)
%o A330129         nX = next((y for y in range(1, 10) if str(oX+x+y)[0] == str(y)), 0)
%o A330129         if nX == 0: break
%o A330129         else: nX += oX + x
%o A330129         if nT == stp:
%o A330129             stp += 100
%o A330129             w1, w2, w3 = w2, w3, nX
%o A330129             if w3 + w1 == 2*w2 and (w3 - w2)%100 == 0:
%o A330129                 it = (nxt(nX) - nX - 1)//(w3 - w2)
%o A330129                 nT += it*100
%o A330129                 nX += (w3 - w2)*it
%o A330129                 w3 = nX
%o A330129                 stp += it*100
%o A330129     return oX
%o A330129 print([a(n) for n in range(1, 30)]) # _Michael S. Branicky_, Nov 18 2023 after _Giovanni Resta_
%Y A330129 Cf. A330128, A121805, A139284, A366492.
%K A330129 nonn,base
%O A330129 1,1
%A A330129 _Giovanni Resta_, Dec 02 2019
%E A330129 Escape clause added to definition by _N. J. A. Sloane_, Nov 14 2023