R. J. Cintra - cp's OEIS frontend

User: R. J. Cintra

R. J. Cintra has authored 2 sequences.

A380421 a(n) is the inverse of 2^3 modulo prime(n).

2, 2, 1, 7, 5, 15, 12, 3, 11, 4, 14, 36, 27, 6, 20, 37, 23, 42, 9, 64, 10, 52, 78, 85, 38, 13, 67, 41, 99, 16, 82, 120, 87, 56, 19, 59, 102, 21, 65, 112, 68, 24, 169, 74, 25, 132, 28, 142, 86, 204, 30, 211, 157, 225, 33, 101, 34, 104, 246, 177, 110, 192, 39, 274

Offset: 2

R. J. Cintra, Jan 25 2025

Robert Israel, Table of n, a(n) for n = 2..10000

Cf. A006254, A292411.

seq(1/8 mod ithprime(n), n=2..65);  # Alois P. Heinz, Feb 14 2025

a[n_] := ModularInverse[8, Prime[n]]; Array[a, 100, 2] (* Amiram Eldar, Feb 05 2025 *)

a(n) = lift(1/Mod(8, prime(n))); \\ Michel Marcus, Jan 25 2025

from sympy import prime
def A380421(n): return pow(8,-1,prime(n)) # Chai Wah Wu, Feb 14 2025

a(n) = 8^(-1) (mod prime(n)) for n >= 2.
a(n) = (A006254(n) * A292411(n)) (mod prime(n)) for n >= 2.
If prime(n) mod 8 = j in {1, 3, 5, 7}, then a(n) = (1 + (8-j)*prime(n))/8. - Robert Israel, Feb 24 2025

A380358 Numbers whose binary expansion ends with 11 and does not contain adjacent zeros.

Original entry on oeis.org

3, 7, 11, 15, 23, 27, 31, 43, 47, 55, 59, 63, 87, 91, 95, 107, 111, 119, 123, 127, 171, 175, 183, 187, 191, 215, 219, 223, 235, 239, 247, 251, 255, 343, 347, 351, 363, 367, 375, 379, 383, 427, 431, 439, 443, 447, 471, 475, 479, 491, 495, 503, 507, 511, 683

Offset: 1

R. J. Cintra, Jan 22 2025

The numbers in this sequence appear in the conversion of conventional binary numbers to the canonical signed-digit representation.

			183 is in the sequence because its binary expansion is 10110111.

J. L. Smith and A. Weinberger, "Shortcut Multiplication for Binary Digital Computers", in Methods for High-Speed Addition and Multiplication, National Bureau of Standards Circular 591, Sec. 1, February, 1958, page 21.

R. J. Cintra, A note on the conversion of nonnegative integers to the canonical signed-digit representation, arXiv:2501.10908 [eess.SP], 2025.

Cf. A003754, A052499, A247648, A365808, A365809.

Select[4*Range[0, 170] + 3, SequencePosition[IntegerDigits[#, 2], {0, 0}] == {} &] (* Amiram Eldar, Feb 05 2025 *)

from itertools import count, islice
def A380358_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:n&3==3 and not '00' in bin(n),count(max(startvalue,1)))
A380358_list = list(islice(A380358_gen(),20)) # Chai Wah Wu, Feb 12 2025

a(n) = 2 * A247648(n) + 1.
From Hugo Pfoertner, Feb 07 2025: (Start)
a(n) = 4*A052499(n) - 1.
a(n) = 4*(A365808(n+1) + 1)/3 - 1.
a(n) = 2*(A365809(n) + 1)/3 - 1. (End)

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User: R. J. Cintra

A380421 a(n) is the inverse of 2^3 modulo prime(n).

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