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 A164321 Let s(n) be the smallest number x such that the decimal representation of n appears as a substring of the decimal representations of the numbers [0...x] more than x times. 2
 199991, 28263828, 371599993, 499999994, 5555555555, 6666666666, 7777777777, 8888888888, 9999999999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(10) <= 10^92 + 10^91 - 90. - Giovanni Resta, Aug 13 2019 LINKS Table of n, a(n) for n=1..9. Tanya Khovanova and Gregory Marton, Archive Labeling Sequences, arXiv:2305.10357 [math.HO], 2023. See p. 4. PROG (Scheme) ;; This is a program in PLT Scheme, a.k.a. mzscheme (define (count-matches re str start-pos) (let ((m (regexp-match-positions re str start-pos))) (if m (+ 1 (count-matches re str (+ (caar m) 1))) 0))) (define (matches-n-in-zero-to-k fn n) (do ((sum-so-far 1) (k (+ n 1)) (re (regexp (format "~a" n)))) ((fn sum-so-far k) k) (when (equal? 0 (modulo k 1000000)) (display (format "~a ~a ~a\n" n k sum-so-far))) (set! k (+ k 1)) (set! sum-so-far (+ sum-so-far (count-matches re (format "~a" k) 0))))) (define (s n) (matches-n-in-zero-to-k > n)) CROSSREFS Closely related to A163500 substituting > for = as suggested by Alexey Radul. The first term is given in the related A092175 which also generalizes the sequence for bases other than 10. Sequence in context: A014778 A094799 A163500 * A230019 A106777 A094800 Adjacent sequences: A164318 A164319 A164320 * A164322 A164323 A164324 KEYWORD nonn,base,more AUTHOR Gregory Marton, Aug 12 2009 STATUS approved

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Last modified September 8 22:43 EDT 2024. Contains 375759 sequences. (Running on oeis4.)