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A341757
Indices of records in A341755 (= length of chain of (k,k+1) sharing a digit with k+(k+1), starting at n).
3
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).
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
Sequence in context: A293042 A159525 A173895 * A286437 A212107 A073979
KEYWORD
nonn,base,more
AUTHOR
M. F. Hasler, Mar 01 2021
EXTENSIONS
a(14)-a(25) from Jinyuan Wang, Mar 13 2021
STATUS
approved