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A139284 Analog of A121805, but starting with 2.

%I A139284 #33 Nov 17 2023 20:13:45
%S A139284 2,24,71,89,180,181,192,214,256,319,413,447,522,547,623,659,756,824,
%T A139284 872,901,920,929,1020,1021,1032,1053,1084,1125,1176,1237,1308,1389,
%U A139284 1480,1481,1492,1513,1544,1585,1636,1697,1768,1849,1940,1941,1952,1973,2005
%N A139284 Analog of A121805, but starting with 2.
%C A139284 It appears that this sequence and A121805 have no terms in common. Furthermore, this sequence exists for at least 1551000000 terms. - _Jacques ALARDET_, Jul 22 2008
%C A139284 The last term of the sequence is a(194697747222394) = 9999999999999918. - _Giovanni Resta_, Nov 30 2019
%D A139284 E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.
%H A139284 Alois P. Heinz, <a href="/A139284/b139284.txt">Table of n, a(n) for n = 1..10000</a>
%H A139284 Carlos Rivera, <a href="https://www.primepuzzles.net/puzzles/puzz_980.htm">Puzzle 980. The "Commas" sequence</a>, The Prime Puzzles and Problems Connection.
%p A139284 a:= proc(n) option remember; local k, t, y; if n=1 then 2 else k:= a(n-1); for y from 0 to 9 do t:= k +10* irem (k, 10) +y; if convert (t, base, 10)[ -1]=y then return t fi od; NULL fi end: seq(a(n), n=1..80); # _Alois P. Heinz_, Aug 13 2009
%t A139284 a[1] = 2; a[n_] := a[n] = For[x=Mod[a[n-1], 10]; y=0, y <= 9, y++, an = a[n-1] + 10*x + y; If[y == IntegerDigits[an][[1]], Return[an]]]; Array[a, 80] (* _Jean-François Alcover_, Nov 25 2014 *)
%o A139284 (Python)
%o A139284 from itertools import islice
%o A139284 def agen(): # generator of terms
%o A139284     an, y = 2, 1
%o A139284     while y < 10:
%o A139284         yield an
%o A139284         an, y = an + 10*(an%10), 1
%o A139284         while y < 10:
%o A139284             if str(an+y)[0] == str(y):
%o A139284                 an += y
%o A139284                 break
%o A139284             y += 1
%o A139284 print(list(islice(agen(), 47))) # _Michael S. Branicky_, Apr 08 2022
%Y A139284 Comma sequences in base 10, starting with 1, 2, 4, 5, 6, 7, 8, 9, 10 are A121805, A139284, A366492, A367337, A367350, A367351, A367352, A367353, A367354. Starting with 3 is trivial, and those starting with 11, 12, 13 are essentially duplicates.
%Y A139284 Cf. A330128, A330129.
%K A139284 nonn,base,fini
%O A139284 1,1
%A A139284 _N. J. A. Sloane_ (based on Angelini's article), Jun 08 2008
%E A139284 More terms from _Alois P. Heinz_, Aug 13 2009