A010885 -id:A010885 - cp's OEIS frontend

A177158 Decimal expansion of (103+2*sqrt(4171))/162.

1, 4, 3, 3, 1, 2, 6, 9, 0, 8, 2, 7, 0, 0, 0, 1, 1, 7, 2, 5, 4, 9, 4, 2, 8, 4, 9, 5, 2, 4, 8, 7, 7, 0, 2, 1, 3, 2, 6, 2, 3, 4, 6, 2, 0, 1, 4, 1, 5, 1, 3, 8, 8, 0, 5, 6, 6, 1, 1, 4, 4, 8, 1, 4, 3, 3, 4, 1, 8, 4, 9, 7, 2, 4, 0, 3, 9, 5, 5, 4, 5, 1, 2, 4, 3, 9, 9, 7, 8, 5, 9, 4, 3, 4, 6, 8, 7, 6, 8, 8, 6, 9, 8, 0, 5

Offset: 1

Klaus Brockhaus, May 03 2010

Continued fraction expansion of (103+2*sqrt(4171))/162 is A010885.

			(103+2*sqrt(4171))/162 = 1.43312690827000117254...

Cf. A177159 (decimal expansion of sqrt(4171)), A010885 (repeat 1, 2, 3, 4, 5, 6).

RealDigits[(103+2*Sqrt[4171])/162,10,120][[1]] (* Harvey P. Dale, Feb 22 2018 *)

A226293 Class of sequences of (p-1)-tuples of reverse order of natural numbers for p = 7.

Original entry on oeis.org

6, 5, 4, 3, 2, 1, 13, 12, 11, 10, 9, 8, 20, 19, 18, 17, 16, 15, 27, 26, 25, 24, 23, 22, 34, 33, 32, 31, 30, 29, 41, 40, 39, 38, 37, 36, 48, 47, 46, 45, 44, 43, 55, 54, 53, 52, 51, 50, 62, 61, 60, 59, 58, 57, 69, 68, 67, 66, 65, 64, 76, 75, 74, 73, 72, 71, 83

Offset: 1

Sam Vaseghi, Jun 02 2013

nonn

Given a prime p, the class of sequences a(n,p) can be constructed from linear combination of the two sequences b(n,p) (A010885) and c(n,p) (A226233), according to a(n,p) = c(n,p)*p - b(n,p) (see Formula below) that ensures uniqueness of the form q = a(n,p)*p^m according to the decomposition theorem Vaseghi 2013 (see link and reference below), for p prime, q a positive integer and m a positive integer or zero. The above example is for p=7. The class is crucial and will be applied to define other number theoretic sequences, that will be submitted to OEIS as well a posterior.

			for p=2: 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,...
for p=3: 2,1,5,4,8,7,11,10,14,13,17,16,20,19,23,22,26,25,29,28,...
for p=5: 4,3,2,1,9,8,7,6,14,13,12,11,19,18,17,16,24,23,22,21,...
for p=7: 6,5,4,3,2,1,13,12,11,10,9,8,20,19,18,17,16,15,27,26,...

S. Vaseghi (alias al-Hwarizmi), Combination of positive integers in terms of primes (sophisticated version 2)

Cf. A166517, A226233.

p = 7; k = p - 1; c = (k + n - 1 - Mod[n - 1, k])/k; b = 1 + Mod[n - 1, k]; Table[c*p - b, {n, 68}]

a(n,p) = c(n,p)*p - b(n,p), where b(n,p) = (1+[(n-1)mod(p-1)]) (see A010885) and c(n,p) = ((p-1)+n-(1+[(n-1)mod(p-1)]))/(p-1) (see A226233), with p = 7.

cp's OEIS Frontend

A177158 Decimal expansion of (103+2*sqrt(4171))/162.

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