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Numbers whose largest decimal digit is 5.
5

%I #35 Sep 08 2022 08:46:18

%S 5,15,25,35,45,50,51,52,53,54,55,105,115,125,135,145,150,151,152,153,

%T 154,155,205,215,225,235,245,250,251,252,253,254,255,305,315,325,335,

%U 345,350,351,352,353,354,355,405,415,425,435,445,450,451,452,453,454

%N Numbers whose largest decimal digit is 5.

%C Numbers n such that A054055(n) = 5.

%C Number of terms less than 10^n is 6^n - 5^n.

%C Subsequence of A011535. - _David A. Corneth_, Mar 25 2017

%C Prime terms are in A106097.

%H Muniru A Asiru, <a href="/A283608/b283608.txt">Table of n, a(n) for n = 1..5000</a>

%t Select[Range[1000], Max[IntegerDigits[#]] == 5 &] (* _Giovanni Resta_, Mar 19 2017 *)

%o (Magma) [n: n in [1..100000] | Maximum(Setseq(Set(Sort(&cat[Intseq(n)])))) eq 5]

%o (PARI) for(n=1, 500, if(vecmax(digits(n))==5, print1(n,", "))) \\ _Indranil Ghosh_, Mar 19 2017

%o (PARI) nxt(n) = {my(d = digits(n), i, j=0, t=0); forstep(i=#d,1,-1, if(d[i]!=5, j=i; break)); if(j>0, d[j]++; if(d[j]==5, for(k=j+1,#d,d[k]=0)); if(j<#d && d[j+1]==5, for(k=j+1,#d-1,d[k]=0)); for(k=1,j-1, if(d[k]==5,for(i=j+1, #d, d[i] = 0);break)), d = vector(#d+1); d[1]=1; d[#d]=5);sum(i=1, #d, d[i]*10^(#d-i))} \\ _David A. Corneth_, Mar 25 2017

%o (Python)

%o from sympy.ntheory.factor_ import digits

%o print([n for n in range(1, 501) if max(digits(n)[1:])==5]) # _Indranil Ghosh_, Mar 19 2017

%o (GAP) Filtered([1..500],n->Maximum(ListOfDigits(n))=5); # _Muniru A Asiru_, Feb 27 2019

%Y Cf. A011535, A054055, A106097.

%Y Cf. Sequences of numbers whose largest decimal digit is k (for k = 1..9): A007088 (k = 1), A277964 (k = 2), A277965 (k = 3), A277966 (k = 4), this sequence (k = 5), A283609 (k = 6), A283610 (k = 7), A283611 (k = 8), A011539 (k = 9).

%K nonn,base,easy

%O 1,1

%A _Jaroslav Krizek_, Mar 19 2017