A367343 -id:A367343 - cp's OEIS frontend

A367344 Compute the commas sequence starting at 1, as in A121805, except do the calculations in octal. The terms are written here in octal (see also A367343).

1, 12, 35, 106, 167, 261, 273, 326, 412, 436, 523, 560, 565, 643, 702, 731, 750, 757, 1050, 1051, 1062, 1103, 1134, 1175, 1246, 1327, 1420, 1421, 1432, 1453, 1504, 1545, 1616, 1677, 1770, 1771, 2003, 2035, 2107, 2201, 2213, 2245, 2317, 2411, 2423, 2455, 2527, 2621, 2633

Offset: 1

N. J. A. Sloane, Nov 15 2023

			The first three terms are 1, 12, 35 in octal, and we check that around the first comma we see 1,1_8 which becomes 11_8 = 9_10, and 1_10 + 9_10 = 10_10 = 12_8 = a(2).
Around the second comma we see 2,3_8, which becomes 23_8 = 19_10, and indeed 12_8 + 23_8 = 10_10 + 19_10 = 29_10 = 35_8 = a(3).

Cf. A121805, A367343.

A367355 Comma sequence, analogous to A121805, starting at 1, but the calculations are done in base 3.

Original entry on oeis.org

1, 5, 12, 13, 17, 25, 29, 36, 37, 41, 48, 49, 53, 61, 66, 68, 76

Offset: 1

N. J. A. Sloane, Nov 18 2023

Cf. A121805, A367343, A367344, A367356.

A367605 and A367605 give the length and last term for the analogous sequence in base b.

# Comma Successor in Maple in base "bas", from N. J. A. Sloane, Dec 06 2023
bas := 3;
Ldigit:=proc(n) local v; v:=convert(n, base, bas); v[-1]; end; # Returns leading digit
# Return comma-successor to a or -1 if no successor exists
commsucc := proc(a) local f,i,d;
f := (a mod bas);
d:=bas*f;
for i from 1 to bas-1 do
d := d+1;
if Ldigit(a+d) = i then return(a+d); fi;
od:
return(-1);
end;
a:=[1]; s:=1; for n from 1 to 16 do s:=commsucc(s); a:=[op(a),s]; od: a;

A367345 Compute the commas sequence starting at 1, as in A121805, except do the calculations in hexadecimal. The terms are written here in decimal.

Original entry on oeis.org

1, 18, 53, 141, 350, 576, 578, 612, 678, 777, 924, 1120, 1124, 1192, 1325, 1539, 1593, 1743, 1990, 2094, 2327, 2448, 2457, 2611, 2669, 2888, 3027, 3087, 3340, 3545, 3703, 3829, 3924, 4003, 4066, 4099, 4148, 4213, 4294, 4391, 4504, 4633, 4778, 4939, 5116, 5309, 5518

Offset: 1

N. J. A. Sloane, Nov 15 2023, following a suggestion from William Cheswick

When written in hexadecimal the terms are 1, 12, 35, 8D, 15E, 240, 242, 264, 2A6, 309, 39C, 460, 464, 4A8, 52D, 603, 639, 6CF, 7C6, 82E, 917, 990, 999, A33, A6D, B48, BD3, C0F, D0C, DD9, ...

Finite with last term a(144693554136426354) = 18446744073709551480, which is FFFFFFFFFFFFFF78 in hexadecimal. - Michael S. Branicky, Nov 18 2023

			See A367344 for examples of similar calculations in base 8.

Michael S. Branicky, Table of n, a(n) for n = 1..100000

Cf. A121805, A367343, A367344.

from itertools import islice
from sympy.ntheory.factor_ import digits
def agen(b=16): # generator of terms
    an, y = 1, 1
    while y < b:
        yield an
        an, y = an + b*(an%b), 1
        while y < b:
            if str(digits(an+y, b)[1]) == str(y):
                an += y
                break
            y += 1
print(list(islice(agen(), 50))) # Michael S. Branicky, Nov 16 2023

cp's OEIS Frontend

A367344 Compute the commas sequence starting at 1, as in A121805, except do the calculations in octal. The terms are written here in octal (see also A367343).

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A367355 Comma sequence, analogous to A121805, starting at 1, but the calculations are done in base 3.

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Maple

A367345 Compute the commas sequence starting at 1, as in A121805, except do the calculations in hexadecimal. The terms are written here in decimal.

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Python