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 11-20 of 20 results.

A061517 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 4.

Original entry on oeis.org

0, 4, 8, 12, 56, 910, 1354, 5798, 9111312, 13555756, 5799911910, 911131313551354, 1355575757995798, 579991191191113139111312, 9111313135513551355575713555756, 135557575799579957999119115799911910
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.

Links

Programs

  • Mathematica
    NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+4)]]&,0,20] (* Harvey P. Dale, Nov 20 2020 *)

Extensions

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

A061520 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 6.

Original entry on oeis.org

0, 6, 12, 78, 1314, 79710, 13151376, 79711791312, 1315137713157978, 797117913137971113151314, 1315137713157979131513777971179710, 797117913137971113151315797117913131315137713151376
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.

Links

Programs

  • Maple
    g:= proc(n) op(convert(n+6,base,10)) end proc:
L[0]:= [0]:
for n from 1 to 12 do L[n]:= map(g,L[n-1]) od:
map(t -> add(t[i]*10^(i-1),i=1..nops(t)), [seq(L[i],i=0..12)]): # Robert Israel, Jan 26 2020
  • Mathematica
    Nest[Append[#, FromDigits@ Flatten@ IntegerDigits[IntegerDigits@ #[[-1]] + 6]] &, {0}, 11] (* Michael De Vlieger, Jan 26 2020 *)
NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+6)]]&,0,15] (* Harvey P. Dale, Jan 10 2021 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001
Corrected by Robert Israel, Jan 26 2020

A061514 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 3.

Original entry on oeis.org

0, 3, 6, 9, 12, 45, 78, 1011, 4344, 7677, 1091010, 43124343, 76457676, 10978109109, 4312101143124312, 7645434476457645, 1097876771097810978, 4312101110910104312101143121011, 76454344431243437645434476454344
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.

Extensions

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

A061515 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 3.

Original entry on oeis.org

1, 4, 7, 10, 43, 76, 109, 4312, 7645, 10978, 43121011, 76454344, 109787677, 431210111091010, 7645434443124343, 10978767776457676, 43121011109101010978109109, 76454344431243434312101143124312, 109787677764576767645434476457645, 431210111091010109781091091097876771097810978
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.

Programs

  • Python
    from itertools import accumulate, repeat
def f(n, _): return int("".join(str(int(d)+3) for d in str(n)))
def aupton(nn): return list(accumulate(repeat(1, nn+1), f))
print(aupton(19)) # Michael S. Branicky, Mar 19 2022

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001
a(17) corrected and a(18), a(19) by Georg Fischer, Mar 19 2022

A061516 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 4.

Original entry on oeis.org

1, 5, 9, 13, 57, 911, 1355, 5799, 9111313, 13555757, 5799911911, 911131313551355, 1355575757995799, 579991191191113139111313, 9111313135513551355575713555757, 135557575799579957999119115799911911
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.

Programs

  • Mathematica
    a[0]=1;a[n_]:=a[n]=FromDigits[Flatten[IntegerDigits/@(IntegerDigits[a[n-1]]+4)]]; Table[a[n],{n,0,15}] (* Zak Seidov, Mar 09 2006 *)

Extensions

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

A061518 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by 5.

Original entry on oeis.org

0, 5, 10, 65, 1110, 6665, 11111110, 66666665, 1111111111111110, 6666666666666665, 11111111111111111111111111111110, 66666666666666666666666666666665, 1111111111111111111111111111111111111111111111111111111111111110
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.

Programs

  • Python
    from itertools import accumulate, repeat
def f(n, _): return int("".join(str(int(d)+5) for d in str(n)))
def aupton(nn): return list(accumulate(repeat(0, nn+1), f))
print(aupton(12)) # Michael S. Branicky, Mar 19 2022

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001
a(3) and following corrected and formula removed by Georg Fischer, Mar 19 2022

A061521 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 6.

Original entry on oeis.org

1, 7, 13, 79, 1315, 79711, 13151377, 79711791313, 1315137713157979, 797117913137971113151315, 1315137713157979131513777971179711, 797117913137971113151315797117913131315137713151377, 131513771315797913151377797117971113151377131579797971179131379711791313
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.

Programs

  • Mathematica
    NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+6)]]&,1,15] (* Harvey P. Dale, May 21 2015 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 11 2001
a(5)-a(12) corrected by Harvey P. Dale, May 21 2015

A061748 a(0) = 1; a(n) is obtained by incrementing each digit of a(n-1) by 8.

Original entry on oeis.org

1, 9, 17, 915, 17913, 91517911, 179139151799, 91517911179139151717, 1791391517999151791117913915915, 91517911179139151717179139151799915179111791317913
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.

Programs

  • Mathematica
    NestList[FromDigits[Flatten[IntegerDigits/@(IntegerDigits[#]+8)]]&,1,10] (* Harvey P. Dale, Aug 20 2012 *)

Extensions

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

A337016 a(0) = 0. Successive terms are double the previous, then with their digits incremented by 1.

Original entry on oeis.org

0, 1, 3, 7, 25, 61, 233, 577, 2265, 5641, 22393, 55897, 2228105, 5567321, 22245753, 555102617, 2221316345, 55537437101, 222185985313, 5554821081737, 222110753274585, 5553326176510281, 22217763464131673, 555466371039374457, 222110438531898591025
Offset: 0

Views

Author

Jamie Robert Creasey, Nov 21 2020

Keywords

Comments

If 9 appears anywhere in the decimal expansion of 2*a(n-1), we replace that digit with 10 upon incrementing by 1. See a(12) of the Examples section and A216556 for more information.

Examples

			To calculate a(12), double 55897 to get 111794, then increment the digits by 1 to get 2228105.
To calculate a(13), double 2228105 to get 4456210, then increment the digits by 1 to get 5567321.

Crossrefs

Cf. A000079, A061511, A089718.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(seq(
      l[-i]+1, i=1..nops(l)))))(convert(2*a(n-1), base, 10)))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Dec 12 2020
  • Mathematica
    NestList[FromDigits[Flatten@ Map[IntegerDigits, IntegerDigits[2 #] + 1]] &, 0, 24] (* Michael De Vlieger, Dec 11 2020 *)
  • PARI
    digs(n) = if (n==0, [0], digits(n));
lista(nn) = {a = 0; print1(a, ", "); for (n=1, nn, a = eval(concat(apply(t->Str(t+1), digs(2*a)))); print1(a, ", "););} \\ Michel Marcus, Nov 28 2020

Formula

a(n) = A216556(2*a(n-1)), a(0) = 0.

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 *)
Previous Showing 11-20 of 20 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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