A283608 Numbers whose largest decimal digit is 5.

5, 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 105, 115, 125, 135, 145, 150, 151, 152, 153, 154, 155, 205, 215, 225, 235, 245, 250, 251, 252, 253, 254, 255, 305, 315, 325, 335, 345, 350, 351, 352, 353, 354, 355, 405, 415, 425, 435, 445, 450, 451, 452, 453, 454

Offset: 1

Author

Jaroslav Krizek, Mar 19 2017

Keywords

• nonn
• base
• easy

Comments

Numbers n such that A054055(n) = 5.

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

Subsequence of A011535. - David A. Corneth, Mar 25 2017

Prime terms are in A106097.

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A011535, A054055, A106097.

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).

Programs

GAP

Filtered([1..500],n->Maximum(ListOfDigits(n))=5); # Muniru A Asiru, Feb 27 2019

Magma

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

Mathematica

Select[Range[1000], Max[IntegerDigits[#]] == 5 &] (* Giovanni Resta, Mar 19 2017 *)

PARI

for(n=1, 500, if(vecmax(digits(n))==5, print1(n,", "))) \\ Indranil Ghosh, Mar 19 2017

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

Python

from sympy.ntheory.factor_ import digits
print([n for n in range(1, 501) if max(digits(n)[1:])==5]) # Indranil Ghosh, Mar 19 2017