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A306331
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Numbers congruent to 6 or 31 mod 38.
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2
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6, 31, 44, 69, 82, 107, 120, 145, 158, 183, 196, 221, 234, 259, 272, 297, 310, 335, 348, 373, 386, 411, 424, 449, 462, 487, 500, 525, 538, 563, 576, 601, 614, 639, 652, 677, 690, 715, 728, 753, 766, 791, 804, 829, 842, 867, 880, 905
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OFFSET
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1,1
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COMMENTS
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A007310(a(n) + 1) is always a multiple of 19.
It equals 5 when n is a term in A273669.
It equals 7 when n is congruent to 3 or 12 (mod 14) but not a term in A273669.
It equals 11 when n is congruent to 4 or 19 (mod 22) but not a case where it equals 5 or 7.
It equals 13 when n is congruent to 5 or 22 (mod 26) (one more than a term in A306285) but not a case where it equals 5, 7, or 11.
It equals 17 when n is congruent to 6 or 29 (mod 34) but not a case where it equals 5, 7, 11, or 13.
For all other cases, it equals 19.
a(n) and (n - 1) have the same remainder (mod 6) (see A010875).
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LINKS
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FORMULA
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G.f.: x*(6 + 25*x + 7*x^2) / ((1 - x)^2*(1 + x)). - Colin Barker, Feb 09 2019
a(n) = a(n - 1) + a(n - 2) - a(n - 3) for n > 3.
a(n) = 19*n - 13 when n is odd and 19*n - 7 when n is even.
a(n) = 19*n - (A040031(n + 1) + 1).
E.g.f.: 7 + (19*x - 10)*exp(x) + 3*exp(-x). - David Lovler, Sep 10 2022
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MAPLE
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seq(seq(38*i+j, j=[6, 31]), i=0..200);
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MATHEMATICA
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Select[Range[200], MemberQ[{6, 31}, Mod[#, 38]] &]
Union[38Range[30] - 32, 38Range[30] - 7] (* Alonso del Arte, Feb 08 2019 *)
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PROG
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(PARI) for(n=6, 905, if((n%38==6) || (n%38==31), print1(n, ", ")))
(PARI) Vec(x*(6 + 25*x + 7*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Feb 09 2019
(Scala) (6 to 1108 by 38).union(31 to 1133 by 38).sorted // Alonso del Arte, Feb 08 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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