A040031 -id:A040031 - cp's OEIS frontend

A010492 Decimal expansion of square root of 38.

6, 1, 6, 4, 4, 1, 4, 0, 0, 2, 9, 6, 8, 9, 7, 6, 4, 5, 0, 2, 5, 0, 1, 9, 2, 3, 8, 1, 4, 5, 4, 2, 4, 4, 2, 2, 5, 2, 3, 5, 6, 2, 4, 0, 2, 3, 4, 4, 4, 5, 7, 4, 5, 4, 4, 8, 7, 4, 5, 7, 2, 0, 7, 2, 4, 5, 8, 3, 9, 9, 6, 5, 0, 2, 6, 3, 6, 6, 4, 2, 1, 2, 9, 6, 6, 7, 2, 9, 7, 9, 9, 1, 9, 8, 8, 9, 9, 9, 4

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 6 followed by {6, 12} repeated. - Harry J. Smith, Jun 04 2009

			6.164414002968976450250192381454244225235624023444574544874572072458399....

Harry J. Smith, Table of n, a(n) for n = 1..20000
Index entries for algebraic numbers, degree 2

Cf. A040031 (continued fraction).

RealDigits[N[Sqrt[38],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2011 *)

default(realprecision, 20080); x=sqrt(38); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010492.txt", n, " ", d));  \\ Harry J. Smith, Jun 04 2009

A306331 Numbers congruent to 6 or 31 mod 38.

Original entry on oeis.org

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

Offset: 1

Davis Smith, Feb 07 2019

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).

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A005408, A005843, A007310, A010875, A020639, A040031, A273669, A306285.

Maple
```
seq(seq(38*i+j, j=[6, 31]), i=0..200);
```

Select[Range[200], MemberQ[{6, 31}, Mod[#, 38]] &]
Union[38Range[30] - 32, 38Range[30] - 7] (* Alonso del Arte, Feb 08 2019 *)

for(n=6, 905, if((n%38==6) || (n%38==31), print1(n, ", ")))

Vec(x*(6 + 25*x + 7*x^2) / ((1 - x)^2*(1 + x)) + O(x^40)) \\ Colin Barker, Feb 09 2019

(6 to 1108 by 38).union(31 to 1133 by 38).sorted // Alonso del Arte, Feb 08 2019

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).
E.g.f.: 7 + (19*x - 10)*exp(x) + 3*exp(-x). - David Lovler, Sep 10 2022

A228838 a(n) = n * A002445(n).

Original entry on oeis.org

0, 6, 60, 126, 120, 330, 16380, 42, 4080, 7182, 3300, 1518, 32760, 78, 12180, 214830, 8160, 102, 34545420, 114, 270600, 37926, 15180, 6486, 1113840, 1650, 41340, 21546, 24360, 10266, 1703601900, 186, 16320, 2135826, 1020, 164010, 5043631320, 222, 1140

Offset: 0

Paul Curtz, Sep 05 2013

nonn

a(n+1) is a multiple of A040031(n+1), sequence of period 2: 6, 12.
a(n) is divisible by A040879(n)=30 followed by the sequence of period 2: 6, 60. See A040214 and A165734.
Note that A164877(n) + A000367(n) = A164558(2n).

			a(0)=0*1, a(1)=1*6, a(2)=2*30=60,, a(3)=3*42=126.

Colin Barker, Table of n, a(n) for n = 0..1000

PARI
```
a(n)=n*denominator(bernfrac(2*n))
```

a(n) = A176328(2n) - A000367(n).
a(n) = A164877(n)/2.
a(n+1) = A111008(n) * A036283(n+1).
2*a(n) = A164558(2n) - A000367(n).
a(n) = A164558(2n) - A176328(2n).

Typo in data fixed by Colin Barker, Jul 03 2015

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A010492 Decimal expansion of square root of 38.

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A306331 Numbers congruent to 6 or 31 mod 38.

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A228838 a(n) = n * A002445(n).

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