cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-15 of 15 results.

A061747 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 8.

Original entry on oeis.org

0, 8, 16, 914, 17912, 91517910, 179139151798, 91517911179139151716, 1791391517999151791117913915914, 91517911179139151717179139151799915179111791317912
Offset: 0

Views

Author

Amarnath Murthy, May 08 2001

Keywords

Comments

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.
Considering each term as a sequence of digits, the subsequences a(2n) and a(2n-1) converge to two different fixed points of the operation, 17913915179... and 915179111791391517.... More precisely, the digits of a(n) except the last are the first digits of a(n+2). - M. F. Hasler, Jun 24 2016
a(16) has 1270 decimal digits. - Michael De Vlieger, Jun 24 2016

Links

Crossrefs

Cf. A061746 - A061750, A061511 - A061522; A061581 - A061587.

Programs

  • Mathematica
    NestList[FromDigits@ Flatten@ Map[IntegerDigits, IntegerDigits[#] + 8] &, 0, 9] (* Michael De Vlieger, Jun 24 2016, after Harvey P. Dale at A061512 *)
  • PARI
    A061747(n=2, a=if(n,8), m=8)={for(n=2, n, a=eval(concat(apply(t->Str(t+m), digits(a))))); a} \\ If only the 2nd argument is given, then the operation is applied once to that argument. - M. F. Hasler, Jun 24 2016

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

A061749 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 9.

Original entry on oeis.org

1, 10, 109, 10918, 109181017, 1091810171091016, 1091810171091016109181091015, 1091810171091016109181091015109181017109181091014
Offset: 0

Views

Author

Amarnath Murthy, May 08 2001

Keywords

Comments

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.
Considering each term as a sequence of digits, this sequence converges to the same limit as A061750, 109181017109101610918109..., fixed point of the operation. - M. F. Hasler, Jun 24 2016

Crossrefs

Cf. A061746 - A061750, A061511 - A061522; A061581 - A061587.

Programs

  • PARI
    A061749(n=1, a=1, m=9)={for(n=1, n, a=eval(concat(apply(t->Str(t+m), digits(a))))); a} \\ If only the 2nd argument is given, then the operation is applied once to that argument. - M. F. Hasler, Jun 24 2016

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

A061513 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 2.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 32, 54, 76, 98, 1110, 3332, 5554, 7776, 9998, 11111110, 33333332, 55555554, 77777776, 99999998, 1111111111111110, 3333333333333332, 5555555555555554, 7777777777777776, 9999999999999998, 11111111111111111111111111111110, 33333333333333333333333333333332
Offset: 0

Views

Author

Amarnath Murthy, May 08 2001

Keywords

Comments

In A061511-A061522, A061746-A061750 when the incremented digit exceeds 9 it is written as a 2-digit string. So 9+1 becomes the 2-digit string 10, etc.
Every term > 8 is made up of only two different consecutive digits, the smaller of which occurs only as the least significant digit.
Otherwise said, these are one less than the odd repdigits (A010785) of length 2^k, cf. formula. - M. F. Hasler, Jun 24 2016

Examples

			Following 32; 3+2 = 5 and 2+2 = 4, hence the next term is 54.

Crossrefs

Cf. A061511 - A061522, A061746 - A061750; A061581 - A061587.

Programs

  • Mathematica
    NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+2)]]&,0,30] (* Harvey P. Dale, Jul 07 2012 *)
  • PARI
    A061513(n)=10^2^(n\5)\9*(n%5*2+1)-1 \\ M. F. Hasler, Jun 24 2016

Formula

a(n) = A061512(n)-1 = (10^2^floor(n/5)-1)/9*(n%5*2+1) - 1, where n%5 means the remainder (in {0..4}) of n divided by 5. - M. F. Hasler, Jun 24 2016

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001

A061580 a(1) = 1, a(n)= number obtained by replacing each digit of a(n-1) with four times its value.

Original entry on oeis.org

1, 4, 16, 424, 16816, 42432424, 1681612816816, 42432424483242432424, 168161281681616321281681612816816, 42432424483242432424424128483242432424483242432424
Offset: 1

Views

Author

Amarnath Murthy, May 13 2001

Keywords

Links

Crossrefs

Cf. A061581, A061582, A061583, A061584, A061585, A061586, A061587.

Programs

  • Mathematica
    NestList[FromDigits@ Flatten@ Map[IntegerDigits, 4*IntegerDigits[#]] &, 1, 9] (* Michael De Vlieger, Feb 25 2023 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Asher Auel, May 15 2001
a(9) corrected by N. J. A. Sloane, Jan 23 2017 at the suggestion of Carolyn Liao.
a(10) corrected by Sean A. Irvine, Feb 25 2023

A338767 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by n.

Original entry on oeis.org

0, 1, 3, 6, 10, 65, 1211, 8988, 16171616, 1015101610151015, 11101115111011161110111511101115, 1212121112121216121212111212121712121211121212161212121112121216
Offset: 0

Views

Author

Jamie Robert Creasey, Nov 07 2020

Keywords

Comments

This sequence is the additive counterpart of the digit factorials which, unlike the digit factorials, increases at a faster pace. A061511 and its relatives bear similarities to this sequence, but each of these increase at varying rates depending on the chosen constant. However, unlike these sequences, the constant increases by 1 each time. If digits within a(n-1) exceed 9 when one adds a constant, we ignore carrying and replace the digit with its correct value, thus 9+1 = 10. a(15) has 1024 digits.

Examples

			a(5) = {1+5, 0+5} = 65, where {x, y} is the concatenation of x and y.
a(6) = {6+6, 5+6} = 1211.

Crossrefs

Cf. A061511-A061750, A061581-A061587, A089718, A337770.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(
      seq(n+l[-i], i=1..nops(l)))))(convert(a(n-1), base, 10)))
    end:
seq(a(n), n=0..12);  # Alois P. Heinz, Nov 15 2020
  • Mathematica
    Nest[Append[#1, FromDigits@ Apply[Join, Map[IntegerDigits, IntegerDigits[#1[[-1]] ] + #2]]] & @@ {#, Length@ #} &, {0}, 11] (* Michael De Vlieger, Nov 13 2020 *)
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