A306277 Numbers congruent to 1 or 8 mod 10.

1, 8, 11, 18, 21, 28, 31, 38, 41, 48, 51, 58, 61, 68, 71, 78, 81, 88, 91, 98, 101, 108, 111, 118, 121, 128, 131, 138, 141, 148, 151, 158, 161, 168, 171, 178, 181, 188, 191, 198, 201, 208, 211, 218, 221, 228, 231, 238, 241, 248, 251, 258, 261, 268, 271, 278, 281, 288, 291, 298, 301, 308, 311, 318, 321

Offset

1,2

Comments

A007310(a(n)+1) is always a multiple of 5.

a(1) = 1, a(n+1) = a(n)+7 when n is odd, a(n+1) = a(n)+3 when n is even.

a(n) mod 6 follows the following pattern: 1,2,5,0,3,4,1,2,5,0,3,4, and so on.

A020639(A007310(a(n)+1)) = 5.

Links

Davis Smith, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 5*n - 2*A000034(n+1).

a(n) = a(n-1) + a(n-2) - a(n-3) for n>3.

a(n) = A273669(n) - 1. - Antti Karttunen, Feb 07 2019

G.f.: x*(1 + 7*x + 2*x^2) / ((1 - x)^2*(1 + x)). - Colin Barker, Feb 09 2019

E.g.f.: 2 + (5*x - 3)*exp(x) + exp(-x). - David Lovler, Sep 07 2022

Sum_{n>=1} (-1)^(n+1)/a(n) = (5+sqrt(5))^(3/2)*phi*Pi/(100*sqrt(2)) + log(phi)/(2*sqrt(5)) + log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023

Maple

seq(seq(10*i+j, j=[1, 8]), i=0..350);

Mathematica

Select[Range[350], MemberQ[{1, 8}, Mod[#, 10]] &]

Prog

(PARI) for(n=1, 350, if((n%10==1) || (n%10==8), print1(n, ", ")))
(PARI) Vec(x*(1 + 7*x + 2*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Feb 09 2019

Crossrefs

Cf. A001622, A020639, A007310, A000034.

Cf. A017281, A017365 (bisections).

One less than A273669.

Sequence in context: A118549 A299979 A291663 * A067469 A237767 A284324

Adjacent sequences: A306274 A306275 A306276 * A306278 A306279 A306280

Keyword

nonn,easy,base

Author

Davis Smith, Feb 02 2019

Status

approved