A112395 -id:A112395 - cp's OEIS frontend

A112435 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 4.

0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 8, 16, 23, 28, 38, 45, 42, 41, 41, 36, 34, 32, 31, 30, 28, 29, 33, 34, 37, 44, 42, 37, 41, 39, 41, 38, 43, 40, 39, 39, 46, 45, 47, 54, 51, 45, 44, 43, 39, 42, 42, 39, 43, 43, 38, 43, 44, 40, 37, 40, 33, 32, 29, 36, 35, 39, 45, 49, 51, 48, 52, 47

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(16)=38 and the loop has 312 terms. It is exactly the same loop as in A112433 "Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 2" and the first term of this 4-loop is the first term of that 2-loop . Computed by Gilles Sadowski.

			a(16)=38 because 4 + 4 + 8 + 1+6 +2+3 + 2+8 = 38

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

Cf. A112395, A004207, A065075, A001370.

nxt[{t_,a_}]:={Take[Join[t,IntegerDigits[Total[t]]],-10],Total[t]}; Join[ {0,0,0,0,0,0,0,0,0},NestList[nxt,{{0,0,0,0,0,0,0,0,0,4},4},80][[All,2]]] (* Harvey P. Dale, Jun 22 2019 *)

A112433 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 2.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 8, 16, 23, 28, 38, 45, 42, 41, 41, 36, 34, 32, 31, 30, 28, 29, 33, 34, 37, 44, 42, 37, 41, 39, 41, 38, 43, 40, 39, 39, 46, 45, 47, 54, 51, 45, 44, 43, 39, 42, 42, 39, 43, 43, 38, 43, 44, 40, 37, 40, 33, 32, 29, 36, 35, 39, 45, 49, 51, 48, 52, 47

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(17)=38 and the loop has 312 terms. It is exactly the same loop as in A112435 "Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 4". Computed by Gilles Sadowski.

			a(17)=38 because 2+2+4+8+1+6+2+3+2+8=38

Cf. A112395.

A112434 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 6, 12, 15, 21, 24, 27, 27, 33, 33, 36, 39, 42, 39, 45, 48, 51, 45, 48, 48, 51, 45, 48, 51, 45, 42, 42, 39, 39, 45, 45, 48, 54, 51, 45, 45, 45, 42, 39, 45, 45, 45, 45, 48, 48, 51, 48, 51, 48, 48, 48, 54, 51, 51, 45, 42, 36, 36, 39, 45, 45, 48, 51

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(21)=36 and the loop has 104 terms. It is the same loop as in A112437 "Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 6" and the first term of this 2-loop is the 59th term of that 6-loop . Computed by Gilles Sadowski.

			a(21)=36 because 2+4 + 2+7 + 2+7 + 3+3 + 3+3 = 36

Cf. A112395.

Example corrected by Harvey P. Dale, May 09 2022

A112437 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 12, 15, 21, 24, 30, 21, 21, 18, 24, 24, 27, 33, 36, 36, 39, 45, 45, 48, 51, 48, 48, 51, 48, 48, 54, 51, 45, 48, 48, 48, 51, 51, 48, 48, 48, 48, 54, 57, 57, 57, 57, 57, 60, 54, 51, 45, 42, 36, 39, 42, 42, 39, 45, 45, 42, 42, 42, 36, 36, 36, 39, 45

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(24)=36 and the loop has 104 terms. It is the same loop as in A112434 "Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 3"; the first term of this 6-loop is the 47th term of that 3-loop and the first term of that 3-loop is the 59th of this 6-loop. Computed by Gilles Sadowski.

			a(24)=36 because 1+8 + 2+4 + 2+4 + 2+7 + 3+3 = 36

Cf. A112395, A004207, A065075, A001370.

A112436 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 5.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 10, 11, 13, 17, 25, 22, 25, 30, 29, 32, 30, 29, 33, 36, 34, 36, 42, 37, 41, 37, 40, 35, 37, 37, 42, 38, 45, 46, 46, 46, 50, 44, 43, 40, 34, 31, 30, 25, 25, 28, 31, 31, 32, 30, 26, 24, 26, 30, 28, 35, 35, 37, 39, 48, 50, 47, 50, 45, 42, 36, 40, 33

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(28)=42 and the loop has 312 terms. Computed by Gilles Sadowski.

			a(28)=42 because 2+9 + 3+3 + 3+6 + 3+4 + 3+6 = 42

Cf. A112395, A004207, A065075, A001370.

A112438 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 14, 19, 29, 40, 44, 38, 44, 42, 37, 43, 42, 37, 39, 45, 44, 45, 48, 50, 43, 41, 38, 40, 32, 32, 30, 28, 27, 32, 32, 32, 34, 31, 26, 29, 35, 38, 42, 44, 44, 41, 38, 38, 43, 42, 40, 39, 40, 33, 32, 31, 31, 23, 24, 24, 25, 28, 34, 36, 39, 45, 47, 48

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(18)=44 and the loop has 312 terms. Computed by Gilles Sadowski.

			a(18)=44 because 1+9 + 2+9 + 4+0 + 4+4 + 3+8 = 44

Cf. A112395, A004207, A065075, A001370.

A112439 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 8.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 16, 23, 28, 38, 49, 46, 49, 57, 59, 62, 57, 59, 60, 54, 49, 54, 51, 43, 44, 43, 37, 38, 43, 43, 42, 41, 36, 34, 34, 34, 35, 38, 40, 37, 40, 37, 39, 40, 40, 34, 37, 37, 35, 39, 47, 51, 47, 48, 52, 47, 47, 52, 48, 48, 53, 50, 44, 45, 42, 36, 37, 42

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(32)=37 and the loop has 312 terms. Computed by Gilles Sadowski.

			a(32)=37 because 5+4 + 5+1 + 4+3 + 4+4 + 4+3 = 37

Cf. A112395, A004207, A065075, A001370.

A112440 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 9.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 18, 27, 36, 45, 54, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45

Offset: 1

Alexandre Wajnberg, Dec 11 2005

Variation on Angelini's A112395. The sequence cycles at a(17)=45 and the loop has one term. Computed by Gilles Sadowski.

			a(17)=45 because 1+8 + 2+7 + 3+6 + 4+5 + 5+4 = 45

Cf. A112395, A004207, A065075, A001370.

A112549 Lengths of the loop of the sequences "Sum of last n digits" beginning with (n-1) zeros followed by digit 3.

Original entry on oeis.org

1, 8, 10, 12, 171, 13, 461, 26, 12203, 104, 318880, 728, 57725, 5804, 6698, 9722

Offset: 1

Alexandre Wajnberg, Dec 17 2005

			a(4)=12 because the sum of last four *digits* of the sequence beginning with 0,0,0,3, (three zeros followed by a 3) enters in a loop whose length is 12 terms; so a(4)=12
a(5)=171 because "Sum of last five digits" beginning with 0,0,0,0,3 enters in a cycle of 171 terms.
Computed by Michael D Beeler.

Cf. A112395.

A112583 Lengths of the loop of the sequences "Sum of last n digits" beginning with (n-1) zeros followed by digit 4.

Original entry on oeis.org

1, 8, 4, 50, 171, 39, 461, 78, 12203, 312, 318880, 2184, 57725, 5804, 1401, 3251

Offset: 1

Alexandre Wajnberg, Dec 17 2005

			a(5)=171 because the sum of last five *digits* of the sequence beginning with 0,0,0,0,4, (four zeros followed by a 4) enters in a loop whose length is 171 terms; so a(5)=171
a(6)=39 because "Sum of last six digits" beginning with 0,0,0,0,0,4 enters in a cycle of 39 terms.
Computed by Michael D Beeler.

Cf. A112395.

cp's OEIS Frontend

A112435 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 4.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A112433 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 2.

Views

Author

Keywords

Comments

Examples

Crossrefs

A112434 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 3.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A112437 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 6.

Views

Author

Keywords

Comments

Examples

Crossrefs

A112436 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 5.

Views

Author

Keywords

Comments

Examples

Crossrefs

A112438 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 7.

Views

Author

Keywords

Comments

Examples

Crossrefs

A112439 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 8.

Views

Author

Keywords

Comments

Examples

Crossrefs

A112440 Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 9.

Views

Author

Keywords

Comments

Examples

Crossrefs

A112549 Lengths of the loop of the sequences "Sum of last n digits" beginning with (n-1) zeros followed by digit 3.

Views

Author

Keywords

Examples

Crossrefs

A112583 Lengths of the loop of the sequences "Sum of last n digits" beginning with (n-1) zeros followed by digit 4.

Views

Author

Keywords

Examples

Crossrefs