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A044482 Numbers k such that the string 4,4 occurs in the base-5 representation of k but not of k+1. 1

%I #29 Jan 28 2022 07:44:24

%S 24,49,74,99,124,149,174,199,224,249,274,299,324,349,374,399,424,449,

%T 474,499,524,549,574,624,649,674,699,724,749,774,799,824,849,874,899,

%U 924,949,974,999,1024,1049,1074,1099,1124,1149

%N Numbers k such that the string 4,4 occurs in the base-5 representation of k but not of k+1.

%C a(n)+1 is divisible by 25 because the string 4,4 must be at the lower end of the base-5 representation. - _Joerg Arndt_, Feb 13 2012

%H Vincenzo Librandi, <a href="/A044482/b044482.txt">Table of n, a(n) for n = 1..1000</a>

%e 49 is in the sequence because its base-5 representation, 144, includes 44 as a substring, but the base-5 representation of 50, 200, does not.

%e 599 is not in the sequence because, although it is 4344 in base 5, 600 is 4400 in base 5.

%t f[n_]:= Length[StringPosition[ToString[FromDigits[IntegerDigits[n,5]]],"44",1]]; Select[Table[n,{n,2000}],f[#]>0&&f[#+1] == 0&] (* _Vincenzo Librandi_, Feb 12 2012 *)

%t SequencePosition[Table[If[SequenceCount[IntegerDigits[n,5],{4,4}]>0,1,0],{n,1200}],{1,0}][[All,1]] (* _Harvey P. Dale_, Aug 20 2021 *)

%Y Cf. A008607 (multiples of 25).

%K nonn,base

%O 1,1

%A _Clark Kimberling_

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)