A306285 Numbers congruent to 4 or 21 mod 26.

4, 21, 30, 47, 56, 73, 82, 99, 108, 125, 134, 151, 160, 177, 186, 203, 212, 229, 238, 255, 264, 281, 290, 307, 316, 333, 342, 359, 368, 385, 394, 411, 420, 437, 446, 463, 472, 489, 498, 515, 524, 541, 550, 567, 576, 593, 602, 619, 628, 645, 654, 671, 680, 697, 706, 723, 732, 749, 758, 775, 784, 801, 810, 827, 836, 853, 862

Offset

1,1

Comments

A007310(a(n)+1) is always a multiple of 13.

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

a(n) mod 4 = A010873(n)

A020639(A007310(a(n)+1) = 5 when n is congruent to 2 or 9 (mod 10) (n is a term in A273669). It equals 7 when n is congruent to 3 or 12 (mod 14) but not congruent to 2 or 9 (mod 10). It equals 11 when n is congruent to 4 or 19 (mod 22) but not congruent to 2 or 9 (mod 10) and not congruent to 3 or 12 (mod 14). Otherwise, it is 13.

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) = 13*n - A010720(n+1).

From Colin Barker, Feb 08 2019: (Start)

G.f.: x*(4 + 17*x + 5*x^2) / ((1 - x)^2*(1 + x)).

a(n) = 13*n - 5 for n even.

a(n) = 13*n - 9 for n odd.

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

E.g.f.: 5 + (13*x - 7)*exp(x) + 2*exp(-x). - David Lovler, Sep 09 2022

Maple

seq(seq(26*i+j, j=[4, 21]), i=0..200);

Mathematica

Select[Range[200], MemberQ[{4, 21}, Mod[#, 26]] &]

Prog

(PARI) for(n=1, 1000, if((n%26==4) || (n%26==21), print1(n, ", ")))
(PARI) Vec(x*(4 + 17*x + 5*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Feb 08 2019

Crossrefs

Cf. A007310, A010720, A020639, A010873, A273669.

Sequence in context: A273270 A273246 A273299 * A273699 A273707 A364679

Adjacent sequences: A306282 A306283 A306284 * A306286 A306287 A306288

Keyword

nonn,easy

Author

Davis Smith, Feb 03 2019

Status

approved