A337572 - OEIS

%I #42 Dec 06 2024 01:37:17

%S 4,9,14,19,20,21,22,23,24,29,34,39,44,45,46,47,48,49,54,59,64,69,70,

%T 71,72,73,74,79,84,89,94,95,96,97,98,99,100,101,102,103,104,105,106,

%U 107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,129,134

%N Numbers having at least one 4 in their representation in base 5.

%C Complementary sequence to A020654.

%H François Marques, <a href="/A337572/b337572.txt">Table of n, a(n) for n = 1..10000</a>

%e 75 is not in the sequence since it is 300_5 in base 5, but 74 is in the sequence since it is 244_5 in base 5.

%p seq(`if`(numboccur(4, convert(n, base, 5))>0, n, NULL), n=0..100);

%t Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 5 ], 4 ]>0)& ]

%o (PARI) isok(m) = #select(x->(x==4), digits(m, 5)) >= 1; \\ _Michel Marcus_, Sep 20 2020

%o (Python)

%o from gmpy2 import digits

%o def A337572(n):

%o     def f(x):

%o         l = (s:=digits(x,5)).find('4')

%o         if l >= 0: s = s[:l]+'3'*(len(s)-l)

%o         return n+int(s,4)

%o     m, k = n, f(n)

%o     while m != k: m, k = k, f(k)

%o     return m # _Chai Wah Wu_, Dec 04 2024

%Y Cf. Numbers with at least one digit b-1 in base b : A074940 (b=3), A337250 (b=4), this sequence (b=5), A333656 (b=6), A337141 (b=7), A337239 (b=8), A338090 (b=9), A011539 (b=10), A095778 (b=11).

%Y Cf. Numbers with no digit b-1 in base b: A005836 (b=3), A023717 (b=4), A020654 (b=5), A037465 (b=6), A020657 (b=7), A037474 (b=8), A037477 (b=9), A007095 (b=10), A171397 (b=11).

%K nonn,base,easy

%O 1,1

%A _François Marques_, Sep 19 2020