

A347295


a(n) = 1 + (a(n1) interpreted as a hexadecimal number); a(1)=1.


0



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 17, 24, 37, 56, 87, 136, 311, 786, 1927, 6440, 25665, 153190, 1388945, 20482374, 541598581, 22571222402, 2359835108355, 621877794997078, 441783186122961017, 1256072821702542102552, 22166920289514371672974675
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OFFSET

1,2


COMMENTS

a(1)=1, and each subsequent term is obtained by interpreting the previous term as a hexadecimal number, converting it into decimal, and incrementing by 1.
This same procedure can be applied to create other baseswitch sequences, e.g., between hexadecimal and octal or between decimal and octal. The base b1 in which a(n1) is interpreted must be larger than the base b2 into which it is converted; otherwise, the b1th term will be b1 written in base b2, which will not be a valid baseb1 expansion (e.g., with b1=10 and b2=16, we would obtain a(10)="A", which is not a valid decimal number).


LINKS



FORMULA

Limit_{n>infinity} log(a(n))/log_10(16)^n = 0.180064331228631629088182553063....  Jon E. Schoenfield, Jan 23 2022


EXAMPLE

a(1)=1;
1_16 = 1_10; 1 + 1 = 2 = a(2);
2_16 = 2_10; 2 + 1 = 3 = a(3);
...
This will continue till a(10)=10, when base differences start to have an effect.
10_16 = 16_10; 16 + 1 = 17 = a(11);
17_16 = 23_10; 23 + 1 = 24 = a(12);
24_16 = 36_10; 36 + 1 = 37 = a(13);
37_16 = 55_10; 55 + 1 = 56 = a(14).


MATHEMATICA

NestList[FromDigits[IntegerDigits[#], 16] + 1 &, 1, 30] (* Amiram Eldar, Jan 23 2022 *)


PROG

(Python)
#Hexdec switch
seq=[]
seq.append(1)
print(seq[0])
for i in range(1, 50):
dec=int(str(seq[i1]), 16)
dec=dec+1
seq.append(dec)
print(seq)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



