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A234023 Positions n where abs(A234022(n)-A234022(n+1)) > 1. 3
47, 51, 59, 67, 75, 79, 175, 179, 187, 195, 203, 207, 291, 299, 339, 347, 419, 427, 467, 475, 531, 539, 611, 619, 659, 667, 739, 747, 767, 771, 779, 815, 831, 847, 883, 891, 899, 907, 943, 959, 975, 1011, 1019, 1027, 1035, 1087, 1139, 1147, 1155, 1163, 1215 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Joerg Arndt, Matters Computational (The Fxtbook), section 1.19, "Invertible transforms on words", pp. 49--55. [This sequence appears on page 50]

EXAMPLE

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.

PROG

(Scheme, with Antti Karttunen's IntSeq-library)

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

(Python)

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

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

def a193231(n):

    if n<2: return n

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

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

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

def ok(n): return 1 if abs(a234022(n) - a234022(n + 1))>1 else 0

print [n for n in range(1, 1501) if ok(n)] # Indranil Ghosh, Jun 05 2017

CROSSREFS

Cf. A234022, A193231.

Sequence in context: A042103 A084366 A257785 * A128940 A243431 A141279

Adjacent sequences:  A234020 A234021 A234022 * A234024 A234025 A234026

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 28 2013

STATUS

approved

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Last modified April 20 09:21 EDT 2021. Contains 343125 sequences. (Running on oeis4.)