A234023 Positions n where abs(A234022(n)-A234022(n+1)) > 1.

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

Offset: 1

Author

Antti Karttunen, Dec 28 2013

Keywords

• nonn

Comments

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

Examples

			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.
		

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]

Crossrefs

Cf. A234022, A193231.

Programs

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 abs(a234022(n) - a234022(n + 1))>1
print([n for n in range(1, 1501) if ok(n)]) # Indranil Ghosh, Jun 05 2017