A139284 Analog of A121805, but starting with 2.

2, 24, 71, 89, 180, 181, 192, 214, 256, 319, 413, 447, 522, 547, 623, 659, 756, 824, 872, 901, 920, 929, 1020, 1021, 1032, 1053, 1084, 1125, 1176, 1237, 1308, 1389, 1480, 1481, 1492, 1513, 1544, 1585, 1636, 1697, 1768, 1849, 1940, 1941, 1952, 1973, 2005

Offset

1,1

Comments

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

The last term of the sequence is a(194697747222394) = 9999999999999918. - Giovanni Resta, Nov 30 2019

References

E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Carlos Rivera, Puzzle 980. The "Commas" sequence, The Prime Puzzles and Problems Connection.

Maple

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

Mathematica

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 *)

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    an, y = 2, 1
    while y < 10:
        yield an
        an, y = an + 10*(an%10), 1
        while y < 10:
            if str(an+y)[0] == str(y):
                an += y
                break
            y += 1
print(list(islice(agen(), 47))) # Michael S. Branicky, Apr 08 2022

Crossrefs

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.

Cf. A330128, A330129.

Sequence in context: A100918 A152965 A345692 * A003614 A195189 A119060

Adjacent sequences: A139281 A139282 A139283 * A139285 A139286 A139287

Keyword

nonn,base,fini

Author

N. J. A. Sloane (based on Angelini's article), Jun 08 2008

Extensions

More terms from Alois P. Heinz, Aug 13 2009

Status

approved