A378472 Position of start of first run of exactly n zeros in the base-2 representation of Pi, or -1 if no such run exists.

17, 1, 26, 7, 109, 135, 96, 189, 2610, 902, 4267, 36139, 17317, 8375, 479166, 11791, 112954, 436893, 1286743, 726844, 5572140, 27456324, 2005750, 42248747, 200643872, 547151636, 171498580, 469458286, 1222711767, 2151391703, 1407238214

Offset: 1

Author

James S. DeArmon, Nov 27 2024

Keywords

• nonn
• base
• more

Comments

In base-2, Pi is: 11.00100100001111110110101010001... For this sequence, the integer part of Pi is ignored, and the first fractional bit is numbered one.

No further terms <= 4*10^9. - Michael S. Branicky, Dec 04 2024

Examples

			The first run of a single "0" bit is at position 17, so a(1) = 17.
The first run of exactly 2 zeros is at position 1, so a(2) = 1.
		

Crossrefs

Cf. A004601, A175945, A178708, A233836.

Programs

Python

import gmpy2
gmpy2.get_context().precision = 2000000
pi = gmpy2.const_pi()
# Convert Pi to binary representation
binary_pi = gmpy2.digits(pi, 2)[0] # zero-th element is the string of bits
outVec = []
for lenRun in range(1,20):
  str0 = "".join( ["0" for _ in range (lenRun)])
  l1 = binary_pi.find("1"+str0+"1")
  outVec.append(l1)
print(outVec)

Formula

a(n) >= A178708(n). - Michael S. Branicky, Dec 13 2024

Extensions

a(21)-a(31) from Michael S. Branicky, Dec 04 2024

Clarified definition, added escape clause - N. J. A. Sloane, Dec 23 2024