A347295 a(n) = 1 + (a(n-1) interpreted as a hexadecimal number); a(1)=1.

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

Offset: 1

Author

Divyanand Valsan, Jan 23 2022

Keywords

• nonn
• base

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 base-switch sequences, e.g., between hexadecimal and octal or between decimal and octal. The base b1 in which a(n-1) is interpreted must be larger than the base b2 into which it is converted; otherwise, the b1-th term will be b1 written in base b2, which will not be a valid base-b1 expansion (e.g., with b1=10 and b2=16, we would obtain a(10)="A", which is not a valid decimal number).

Examples

			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).
		

Crossrefs

Cf. A102489.

Programs

Mathematica

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

Python

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

Formula

a(n) = A102489(a(n-1)) + 1. - Jon E. Schoenfield, Jan 23 2022

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