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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A045373 (primes), A047346, A047352.

Complement of A047327.

Programs

Magma

[n : n in [0..150] | n mod 7 in [0, 1, 2, 4]]; // Wesley Ivan Hurt, Jun 01 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 *)

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

Formula

If n mod 4 = 0 then a(n) = floor((7*n-3)/4)+1, else a(n) = floor((7*n-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