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 A306331 Numbers congruent to 6 or 31 mod 38. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A007310(a(n) + 1) is always a multiple of 19. A020639(A007310(a(n) + 1)) = 5, 7, 11, 13, 17, or 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). LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA 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 - 10 + 3*(-1)^n. - Wesley Ivan Hurt, Mar 10 2019 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). MAPLE seq(seq(38*i+j, j=[6, 31]), i=0..200); MATHEMATICA Select[Range, MemberQ[{6, 31}, Mod[#, 38]] &] Union[38Range - 32, 38Range - 7] (* Alonso del Arte, Feb 08 2019 *) PROG (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 CROSSREFS Cf. A005408, A005843, A007310, A010875, A020639, A040031, A273669, A306285. Sequence in context: A156825 A043058 A155097 * A254502 A025524 A042841 Adjacent sequences:  A306328 A306329 A306330 * A306332 A306333 A306334 KEYWORD nonn,easy AUTHOR Davis Smith, Feb 07 2019 STATUS approved

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Last modified January 20 04:53 EST 2021. Contains 340301 sequences. (Running on oeis4.)