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

%I A347295 #36 Mar 05 2022 01:23:59
%S A347295 1,2,3,4,5,6,7,8,9,10,17,24,37,56,87,136,311,786,1927,6440,25665,
%T A347295 153190,1388945,20482374,541598581,22571222402,2359835108355,
%U A347295 621877794997078,441783186122961017,1256072821702542102552,22166920289514371672974675
%N A347295 a(n) = 1 + (a(n-1) interpreted as a hexadecimal number); a(1)=1.
%C A347295 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.
%C A347295 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).
%F A347295 a(n) = A102489(a(n-1)) + 1. - _Jon E. Schoenfield_, Jan 23 2022
%F A347295 Limit_{n->infinity} log(a(n))/log_10(16)^n = 0.180064331228631629088182553063.... - _Jon E. Schoenfield_, Jan 23 2022
%e A347295 a(1)=1;
%e A347295 1_16 = 1_10; 1 + 1 = 2 = a(2);
%e A347295 2_16 = 2_10; 2 + 1 = 3 = a(3);
%e A347295 ...
%e A347295 This will continue till a(10)=10, when base differences start to have an effect.
%e A347295 10_16 = 16_10; 16 + 1 = 17 = a(11);
%e A347295 17_16 = 23_10; 23 + 1 = 24 = a(12);
%e A347295 24_16 = 36_10; 36 + 1 = 37 = a(13);
%e A347295 37_16 = 55_10; 55 + 1 = 56 = a(14).
%t A347295 NestList[FromDigits[IntegerDigits[#], 16] + 1 &, 1, 30] (* _Amiram Eldar_, Jan 23 2022 *)
%o A347295 (Python)
%o A347295 #Hex-dec switch
%o A347295 seq=[]
%o A347295 seq.append(1)
%o A347295 print(seq[0])
%o A347295 for i in range(1,50):
%o A347295     dec=int(str(seq[i-1]), 16)
%o A347295     dec=dec+1
%o A347295     seq.append(dec)
%o A347295 print(seq)
%Y A347295 Cf. A102489.
%K A347295 nonn,base
%O A347295 1,2
%A A347295 _Divyanand Valsan_, Jan 23 2022