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

Author

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

Keywords

• nonn
• base
• fini

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.

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.

Programs

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 *)

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

Extensions

More terms from Alois P. Heinz, Aug 13 2009