A341756 Records in A341755 (= length of chain of (k,k+1) sharing a digit with k+(k+1), starting at n).

2, 5, 6, 20, 28, 48, 170, 274, 350, 1670, 2731, 3350, 16670, 27274, 33350, 166670, 272731, 333350, 1666670, 2727274, 3333350, 16666670, 27272731, 33333350, 166666670

Offset

1,1

Comments

The indices of these records, i.e., k such that a(n) = A341755(k) > A341755(m) for all m < k, are listed in A341757.

Links

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

Formula

a(n) = A341755(A341757(n)).

Conjecture: | a(n+3)/10 - a(n) | <= 10 for all n except n = 6; specifically:

a(3n+6) = 3...350 with n '3's, n >= 1;

a(3n+7) = 16...670 with n '6's, n >= 0.

Example

After {0, 1}, the first nontrivial chain is {9, 10, 11, 12, 13} with 5 members.
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, t); for(k=0, nn, if(t=A341755(k), if(t>m, print1(m=t, ", ")); k+=t-1)) \\ modified by Jinyuan Wang, Mar 13 2021

Crossrefs

Cf. A341755, A341757.

Sequence in context: A282536 A248719 A184594 * A014454 A136324 A128367

Adjacent sequences: A341753 A341754 A341755 * A341757 A341758 A341759

Keyword

nonn,base,more

Author

M. F. Hasler, Mar 01 2021

Extensions

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

Status

approved