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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[200], MemberQ[{6, 31}, Mod[#, 38]] &]

Union[38Range[30] - 32, 38Range[30] - 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.)