A367356 -id:A367356 - cp's OEIS frontend

A367598 Record high-points in A367356.

Original entry on oeis.org

17, 164, 490, 1472, 39819, 119228, 3225387, 9657464, 261256395, 782254580, 21161768043

Offset: 1

N. J. A. Sloane, Nov 24 2023

This is the base-3 analog of A367364.

Cf. A121805, A367355, A367356, A367364, A367599.

a(7)-a(11) from Michael S. Branicky, Nov 27 2023

A367599 Indices of record high-points in A367356.

Original entry on oeis.org

1, 6, 7, 18, 162, 1458, 13122, 118098, 1062882, 9565938, 86093442

Offset: 1

N. J. A. Sloane, Nov 24 2023

This is a base-3 analog of A367365. The present sequence includes the terms 2*3, 2*3^2, 2*3^6, whereas A367365 includes 4*10 and 4*10^3.

Terms a(4)-a(11) are of the form 2*3^(2*i), i > 0. - Michael S. Branicky, Nov 26 2023

Cf. A121805, A367355, A367356, A367364, A367598.

a(7)-a(11) from Michael S. Branicky, Nov 27 2023

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;

A367606 Comma-successor to n working in base 3, but written in base 10, or -1 if n has no successor.

Original entry on oeis.org

5, 9, 4, -1, 12, 8, 11, 15, 10, 14, 19, 13, 17, 22, 16, 21, 25, 20, 24, 27, 23, -1, 30, 26, 29, 33, 28, 32, 36, 31, 35, 39, 34, 38, 42, 37, 41, 45, 40, 44, 48, 43, 47, 51, 46, 50, 55, 49, 53, 58, 52, 57, 61, 56, 60, 64, 59, 63, 67, 62, 66, 70, 65, 69, 73, 68, 72, 76, 71, 75, 79, 74, 78, 81, 77, -1, 84, 80, 83, 87, 82

Offset: 1

N. J. A. Sloane, Dec 11 2023

This is a base-3 analog of A367338.
It seems that the indices of the terms equal to -1 are in A168613. - Ivan N. Ianakiev, Dec 12 2023
This is true for A168613(n), n >= 2.  See proofs in A367341. - Michael S. Branicky, Dec 15 2023

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A121085, A168613, A367338, A367341, A367355, A367356, A367607, A367608, A367609.

from sympy.ntheory.factor_ import digits
def a(n):
    b = n + 3*(n%3)
    return next((b+y for y in [1, 2] if digits(b+y, 3)[1] == y), -1)
print([a(n) for n in range(1, 82)]) # Michael S. Branicky, Dec 11 2023

A367609 Comma-number associated with A367607(n), and written in base 3, or -1 if A367607(n) = -1.

Original entry on oeis.org

11, 21, 1, -1, 21, 2, 11, 21, 1, 11, 22, 1, 11, 22, 1, 12, 22, 2, 12, 21, 2, -1, 21, 2, 11, 21, 1, 11, 21, 1, 11, 21, 1, 11, 21, 1, 11, 21, 1, 11, 21, 1, 11, 21, 1, 11, 22, 1, 11, 22, 1, 12, 22, 2, 12, 22, 2, 12, 22, 2, 12, 22, 2, 12, 22, 2, 12, 22, 2, 12, 22, 2, 12, 21, 2, -1, 21, 2, 11, 21, 1, 11, 21, 1, 11, 21, 1, 11, 21, 1, 11, 21, 1, 11, 21, 1, 11, 21, 1, 11

Offset: 1

N. J. A. Sloane, Dec 11 2023

This is a base-3 analog of A367339.

Michael S. Branicky, Table of n, a(n) for n = 1..10000
Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, arXiv:2401.14346, Youtube

Cf. A121085, A367339, A367355, A367356, A367606-A367608.

from sympy.ntheory.factor_ import digits
def a(n):
    b = n + 3*(n%3)
    return next((int("".join(map(str, digits(b+y-n, 3)[1:]))) for y in [1, 2] if digits(b+y, 3)[1] == y), -1)
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Dec 11 2023

A367608 Comma-number associated with A367606(n), but written in base 10, or -1 if A367606(n) = -1.

Original entry on oeis.org

4, 7, 1, -1, 7, 2, 4, 7, 1, 4, 8, 1, 4, 8, 1, 5, 8, 2, 5, 7, 2, -1, 7, 2, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 8, 1, 4, 8, 1, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 7, 2, -1, 7, 2, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4

Offset: 1

N. J. A. Sloane, Dec 11 2023

If n has a comma-successor m (say) in base 3, then a(n) is the comma-number linking n and m, and is equal to m-n; a(n) = -1 if n has no successor. See A367338 for definitions.

This is a base-3 analog of A367339.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A121085, A367339, A367355, A367356, A367606-A367609.

from sympy.ntheory.factor_ import digits
def a(n):
    b = n + 3*(n%3)
    return next((b+y-n for y in [1, 2] if digits(b+y, 3)[1] == y), -1)
print([a(n) for n in range(1, 101)]) # Michael S. Branicky, Dec 11 2023

A367607 Comma-successor to n working in base 3, and written in base 3, or -1 if n has no successor.

Original entry on oeis.org

12, 100, 11, -1, 110, 22, 102, 120, 101, 112, 201, 111, 122, 211, 121, 210, 221, 202, 220, 1000, 212, -1, 1010, 222, 1002, 1020, 1001, 1012, 1100, 1011, 1022, 1110, 1021, 1102, 1120, 1101, 1112, 1200, 1111, 1122, 1210, 1121, 1202, 1220, 1201, 1212, 2001, 1211, 1222, 2011, 1221, 2010, 2021, 2002, 2020, 2101, 2012, 2100

Offset: 1

N. J. A. Sloane, Dec 11 2023

This is a base-3 analog of A367338.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A121085, A007089, A367338, A367355, A367356, A367606, A367608, A367609.

from sympy.ntheory.factor_ import digits
def a(n):
    b = n + 3*(n%3)
    return next((int("".join(map(str, d3))) for y in [1, 2] if (d3:=digits(b+y, 3)[1:])[0] == y), -1)
print([a(n) for n in range(1, 61)]) # Michael S. Branicky, Dec 11 2023

A367623 Number of comma-children of n in base 3.

Original entry on oeis.org

2, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

N. J. A. Sloane, Dec 23 2023

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A121805, A367355, A367356, A367606-A367609, A367622.

from sympy.ntheory.factor_ import digits
def a(k, base=3):
    m = k + base*(k%base)
    return len([m+y for y in range(1, base) if digits(m+y, base)[1] == y])
print([a(n) for n in range(1, 96)]) # Michael S. Branicky, Dec 23 2023

cp's OEIS Frontend

A367598 Record high-points in A367356.

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A367599 Indices of record high-points in A367356.

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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

A367606 Comma-successor to n working in base 3, but written in base 10, or -1 if n has no successor.

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Python

A367609 Comma-number associated with A367607(n), and written in base 3, or -1 if A367607(n) = -1.

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Python

A367608 Comma-number associated with A367606(n), but written in base 10, or -1 if A367606(n) = -1.

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Python

A367607 Comma-successor to n working in base 3, and written in base 3, or -1 if n has no successor.

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Python

A367623 Number of comma-children of n in base 3.

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Python