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A306285
Numbers congruent to 4 or 21 mod 26.
3
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.
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
KEYWORD
nonn,easy
AUTHOR
Davis Smith, Feb 03 2019
STATUS
approved