A044072 Numbers k such that string 2,3 occurs in the base 4 representation of k but not of k-1.

11, 27, 43, 59, 75, 91, 107, 123, 139, 155, 171, 203, 219, 235, 251, 267, 283, 299, 315, 331, 347, 363, 379, 395, 411, 427, 459, 475, 491, 507, 523, 539, 555, 571, 587, 603, 619, 635, 651, 667, 683, 779, 795, 811, 827, 843, 859, 875, 891, 907, 923, 939, 971

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Members are of form 16k+11, but not all such numbers are in the sequence. The first missing number is 187.

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Differs from A106839.

Cf. A044453.

Programs

Mathematica

Flatten[Position[Partition[Table[If[MemberQ[Partition[IntegerDigits[n, 4], 2, 1], {2, 3}], 1, 0], {n, 1000}], 2, 1], {0, 1}]] + 1 (* Vincenzo Librandi, Aug 19 2015 *)

Python

from sympy.ntheory.factor_ import digits
def has23(n): return "23" in "".join(map(str, digits(n, 4)[1:]))
def ok(n): return has23(n) and not has23(n-1)
print([k for k in range(972) if ok(k)]) # Michael S. Branicky, Nov 27 2021

Extensions

a(48) and beyond from Michael S. Branicky, Nov 27 2021