A047351 Numbers that are congruent to {0, 1, 2, 4} mod 7.

0, 1, 2, 4, 7, 8, 9, 11, 14, 15, 16, 18, 21, 22, 23, 25, 28, 29, 30, 32, 35, 36, 37, 39, 42, 43, 44, 46, 49, 50, 51, 53, 56, 57, 58, 60, 63, 64, 65, 67, 70, 71, 72, 74, 77, 78, 79, 81, 84, 85, 86, 88, 91, 92, 93, 95, 98, 99, 100, 102, 105, 106, 107, 109, 112

Offset

1,3

Comments

The set of values for m such that 7i+m is a perfect square (the quadratic residues of 7 including the trivial case of k*7). - Gary Detlefs, Mar 07 2010

The product of any two terms belongs to the sequence and therefore also a(n)^2, a(n)^3, a(n)^4 etc. - Bruno Berselli, Dec 03 2012

Links

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

If n mod 4 = 0 then a(n) = floor(7n-3)/4)+1, else a(n) = floor(7n-3)/4). [Gary Detlefs, Mar 07 2010]

G.f.: x^2*(1+x+2*x^2+3*x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

a(n) = n-3+(6*n+(2-(-1)^n)(1-2*i^(n(n+1)))+1)/8, where i=sqrt(-1). - Bruno Berselli, Dec 03 2012

a(0)=0, a(1)=1, a(2)=2, a(3)=4, a(4)=7, a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Harvey P. Dale, Jun 04 2013

a(2k) = A047346(k), a(2k-1) = A047352(k). - Wesley Ivan Hurt, Jun 01 2016

E.g.f.: (12 + 3*sin(x) - cos(x) + (7*x - 10)*sinh(x) + (7*x - 11)*cosh(x))/4. - Ilya Gutkovskiy, Jun 02 2016

Maple

for i from 1 to 56 do if(i mod 4=0) then print(floor(7*i-3)/4)+1) else print(floor(7*i-3)/4)) fi od; # Gary Detlefs, Mar 07 2010
A047351:=n->n-3+(6*n+(2-I^(2*n))*(1-2*I^(n*(n+1)))+1)/8: seq(A047351(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 2, 4}, Mod[#, 7]]&] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 4, 7}, 60] (* Harvey P. Dale, Jun 04 2013 *)

Prog

(Magma) [n : n in [0..150] | n mod 7 in [0, 1, 2, 4]]; // Wesley Ivan Hurt, Jun 01 2016
(PARI) x='x+O('x^100); concat(0, Vec(x^2*(1+x+2*x^2+3*x^3)/((1+x)*(1+x^2)*(x-1)^2))) \\ Altug Alkan, Jun 02 2016

Crossrefs

Cf. A045373 (primes), A047346, A047352.

Complement of A047327.

Sequence in context: A352246 A359585 A035261 * A242937 A247979 A028951

Adjacent sequences: A047348 A047349 A047350 * A047352 A047353 A047354

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved