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A047219
Numbers that are congruent to {1, 3} mod 5.
34
1, 3, 6, 8, 11, 13, 16, 18, 21, 23, 26, 28, 31, 33, 36, 38, 41, 43, 46, 48, 51, 53, 56, 58, 61, 63, 66, 68, 71, 73, 76, 78, 81, 83, 86, 88, 91, 93, 96, 98, 101, 103, 106, 108, 111, 113, 116, 118, 121, 123, 126, 128, 131, 133, 136, 138, 141, 143, 146, 148
OFFSET
1,2
COMMENTS
A001844(N)= N^2 + (N+1)^2 is divisible by 5 if and only if N=a(n), n>=1. E.g., n=2: 5|(9 + 16), but 7^2 + 8^2 is not congruent 0 (mod 5). - Wolfdieter Lang, May 09 2012
The number of partitions of 5*(n-1) into at most 2 parts. - Colin Barker, Mar 31 2015
FORMULA
a(n) = floor((5*n-3)/2). - Santi Spadaro, Jul 24 2001, corrected by Gary Detlefs, Oct 28 2011
G.f.: x*(1 + 2*x + 2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 07 2011
a(n) = 2*n + floor((n-1)/2) - 1. - Arkadiusz Wesolowski, Sep 19 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1/2 + sqrt(5)/10)*Pi/5 + log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021
E.g.f.: 2 + ((10*x - 7)*exp(x) - exp(-x))/4. - David Lovler, Aug 23 2022
MATHEMATICA
Flatten[#+{1, 3}&/@(5*Range[0, 30])] (* Harvey P. Dale, Dec 22 2013 *)
PROG
(PARI) a(n)=(5*n-3)\2 \\ Charles R Greathouse IV, Oct 28 2011
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved