A341757 Indices of records in A341755 (= length of chain of (k,k+1) sharing a digit with k+(k+1), starting at n).

0, 9, 48, 94, 239, 486, 944, 2393, 4886, 9444, 23936, 48886, 94444, 239393, 488886, 944444, 2393936, 4888886, 9444444, 23939393, 48888886, 94444444, 239393936, 488888886, 944444444

Offset

1,2

Comments

The corresponding record values A341755(a(n)) are listed as A341756(n).

Links

Table of n, a(n) for n=1..25.

Formula

Conjecture: | a(3n+3)/10 - a(3n) | <= 1 for n >= 1; specifically:

a(3n + 1) = 9*10^n + 4*(10^n-1)/9 (= 94...4 with n '4's), and

a(3n + 3) = 48...86 with n '8's, for n >= 1.

Example

After the chain {0, 1} of length A341756(1) = A341755(0) = 2 starting at a(1) = 0, the first nontrivial chain is {9, 10, 11, 12, 13} with A341756(1) = 5 members starting at a(2) = 9.
The chain of length 48 starting at 486 contains a somewhat "trivial" chain starting at 500: the shared digit of the first 10 terms is the '0' of 10** and 50*, the shared digit of the next 10-11 terms is the '1' of 10** and 51*.

Prog

(PARI) lista(nn) = my(m=0, t); for(k=0, nn, if(t=A341755(k), if(t>m, print1(k, ", "); m=t); k+=t-1)) \\ modified by Jinyuan Wang, Mar 13 2021

Crossrefs

Cf. A341755, A341756.

Sequence in context: A293042 A159525 A173895 * A286437 A212107 A073979

Adjacent sequences: A341754 A341755 A341756 * A341758 A341759 A341760

Keyword

nonn,base,more

Author

M. F. Hasler, Mar 01 2021

Extensions

a(14)-a(25) from Jinyuan Wang, Mar 13 2021

Status

approved