A234023 - OEIS

%I #21 May 08 2021 11:24:52

%S 47,51,59,67,75,79,175,179,187,195,203,207,291,299,339,347,419,427,

%T 467,475,531,539,611,619,659,667,739,747,767,771,779,815,831,847,883,

%U 891,899,907,943,959,975,1011,1019,1027,1035,1087,1139,1147,1155,1163,1215

%N Positions n where abs(A234022(n)-A234022(n+1)) > 1.

%C These are the indices to A193231 where the count of 1-bits in its terms changes by more than one.

%H Antti Karttunen, <a href="/A234023/b234023.txt">Table of n, a(n) for n = 1..10000</a>

%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 1.19, "Invertible transforms on words", pp. 49--55. [This sequence appears on page 50]

%e 47 is in the sequence, as A193231(47) = 59, A193231(48) = 34, and A007088(59)='111011', A007088(34)='100010', thus there are five 1-bits in the former, while there are only two in the latter, and abs(5-2) = 3 > 1.

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A234023 (MATCHING-POS 1 1 (lambda (n) (> (abs (- (A234022 n) (A234022 (+ n 1)))) 1))))

%o (Python)

%o def a065621(n): return n^(2*(n - (n&-n)))

%o def a048724(n): return n^(2*n)

%o def a193231(n):

%o     if n<2: return n

%o     if n%2==0: return a048724(a193231(n//2))

%o     else: return a065621(1 + a193231((n - 1)//2))

%o def a234022(n): return bin(a193231(n))[2:].count("1")

%o def ok(n): return abs(a234022(n) - a234022(n + 1))>1

%o print([n for n in range(1, 1501) if ok(n)]) # _Indranil Ghosh_, Jun 05 2017

%Y Cf. A234022, A193231.

%K nonn

%O 1,1

%A _Antti Karttunen_, Dec 28 2013