A211821 -id:A211821 - cp's OEIS frontend

A211822 Nonprime numbers with all divisors with additive digital root of 1.

1, 361, 703, 1369, 1387, 2071, 2413, 2701, 3097, 3439, 3781, 4033, 4699, 5149, 5329, 5833, 6031, 6697, 6859, 7201, 7363, 7543, 7957, 8227, 9253, 9271, 9937, 10027, 10279, 10963, 11359, 11647, 11881, 11899, 11989, 13213, 13357

Offset: 1

Jaroslav Krizek, Apr 26 2012

Complement of A061237 (prime numbers == 1 (mod 9)) with respect to A211821.

			Number 6859 with divisors 1, 19, 361, 6859 is in sequence because all divisors have additive digital root of 1.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A211821, A024906, A061237, A017173, A211823.

filter:= n -> not isprime(n) and numtheory:-factorset(n) mod 9 = {1}:
filter(1):= true:
select(filter, [seq(i,i=1..20000,9)]); # Robert Israel, May 10 2020

(* First run the program for A211821 *) Select[A211821, Not[PrimeQ[#]] &] (* Alonso del Arte, May 02 2012 *)

A211823 Numbers k such that 9*k+1 are numbers with all divisors with additive digital root = 1.

Original entry on oeis.org

0, 2, 4, 8, 12, 14, 18, 20, 22, 30, 34, 40, 42, 44, 48, 54, 58, 60, 64, 68, 70, 78, 82, 84, 90, 92, 98, 102, 104, 110, 112, 118, 124, 128, 130, 142, 144, 152, 154, 158, 162, 170, 172, 174, 180, 184, 188, 194, 198, 200, 208, 222, 224, 228, 230, 232, 238, 240, 242

Offset: 1

Jaroslav Krizek, Apr 26 2012

Numbers of form 9*k+1 with all divisors with digital root = 1 is in A211821.

Supersequence of A024906 (numbers n such that 9*n+1 is prime).

			Number k = 40 is in sequence because number 9*40 + 1 = 361 is number with all divisors (1, 19, 361) with additive digital root = 1.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A211821, A024906, A061237, A017173, A211822

adrQ[n_]:=NestWhile[Total[IntegerDigits[#]]&,n,#>9&]==1; Select[Range[ 0,250],AllTrue[Divisors[9#+1],adrQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 27 2020 *)

Corrected (230 inserted) by Harvey P. Dale, Aug 27 2020

A216755 Digital root of the fifth power of Fibonacci(n).

Original entry on oeis.org

1, 1, 5, 9, 2, 8, 7, 9, 4, 1, 8, 9, 8, 8, 4, 9, 7, 1, 2, 9, 5, 8, 1, 9, 1, 1, 5, 9, 2, 8, 7, 9, 4, 1, 8, 9, 8, 8, 4, 9, 7, 1, 2, 9, 5, 8, 1, 9, 1, 1, 5, 9, 2, 8, 7, 9, 4, 1, 8, 9, 8, 8, 4, 9, 7, 1, 2, 9, 5, 8, 1, 9, 1, 1, 5, 9, 2, 8, 7, 9, 4, 1, 8, 9, 8, 8, 4, 9, 7, 1, 2, 9, 5, 8, 1, 9, 1, 1, 5, 9

Offset: 1

Ravi Bhandari, Sep 15 2012

This sequence is periodic with period 24, i.e. gcd(period of digital roots of squares of Fibonacci, period of digital roots of cubes of Fibonacci)

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1).

Cf. A030132, A216676, A216699

(* First run program for A211821 to define digitalRoot *) Table[digitalRoot[Fibonacci[n]^5], {n, 90}] (* Alonso del Arte, Sep 15 2012 *)
LinearRecurrence[{0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1},{1, 1, 5, 9, 2, 8, 7, 9, 4, 1, 8, 9, 8, 8, 4, 9},100] (* Ray Chandler, Aug 27 2015 *)

a(n) = A010888(A056572(n)).
a(n) = a(n-4) - a(n-12) + a(n-16). - R. J. Mathar, Sep 15 2012
G.f. x*( -1-x-5*x^2-9*x^3-x^4-7*x^5-2*x^6-2*x^8+7*x^9-x^10-5*x^12-8*x^13-x^14-9*x^15 ) / ( (x-1) *(1+x) *(x^2+1) *(x^4+1) *(x^8-x^4+1) ). - R. J. Mathar, Sep 15 2012

cp's OEIS Frontend

A211822 Nonprime numbers with all divisors with additive digital root of 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

A211823 Numbers k such that 9*k+1 are numbers with all divisors with additive digital root = 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A216755 Digital root of the fifth power of Fibonacci(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula