A367341 -id:A367341 - cp's OEIS frontend

A367615 Numbers that have a comma-successor.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75

Offset: 1

N. J. A. Sloane, Dec 18 2023

This is the complement to A367341.
The actual successors are given in A367340.
See A367338 for definition.

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, Fibonacci Quarterly 62:3 (2024), 215-232.
Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, Local copy.
N. J. A. Sloane, Eric Angelini's Comma Sequence, Experimental Math Seminar, Rutgers Univ., January 18, 2024, Youtube video; Slides

Cf. A121805, A367338, A367340, A367341

fQ[n_]:=Module[{k=n+10*Last[IntegerDigits[n]]+Range[9]},Select[k,#-n==FromDigits[{Last[IntegerDigits[n]],First[IntegerDigits[#]]}]&]]!={};
Select[Range[75],fQ[#]&] (* Ivan N. Ianakiev, Dec 18 2023 *)

More terms from Michael S. Branicky, Dec 18 2023

A367645 Lexicographically earliest sequence of distinct positive numbers with the property that the sequence formed by the pairs of digits adjacent to the commas between the terms equals the magnitude of the successive differences between the terms.

Original entry on oeis.org

1, 12, 35, 94, 135, 78, 159, 63, 30, 28, 109, 18

Offset: 1

Scott R. Shannon and Eric Angelini, Nov 25 2023

The sequence is finite; after twelve terms 18 is reached which has no following term - see A367341.

			a(6) = 78 as a(5) = 135, and |78 - 135| = 57 which can be formed from the last digit of 135 and the first digit of 78.
a(12) = 18 as a(11) = 109, and |18 - 109| = 91 which can be formed from the last digit of 109 and the first digit of 18. See A367341 for a proof that no following term can exist.

Cf. A121805, A367341, A367635.

cp's OEIS Frontend

A367615 Numbers that have a comma-successor.

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