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.

Showing 1-9 of 9 results.

A099534 a(n)=Sum of the first n decimal places of e.

Original entry on oeis.org

7, 8, 16, 18, 26, 27, 35, 37, 45, 49, 54, 63, 63, 67, 72, 74, 77, 82, 85, 91, 91, 93, 101, 108, 112, 119, 120, 123, 128, 130, 136, 142, 144, 148, 157, 164, 171, 176, 183, 185, 189, 196, 196, 205, 208, 214, 223, 232, 241, 246, 255, 260, 267, 271, 280, 286, 292
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 22 2004

Keywords

Examples

			Decimal places of e are: 718281828459045... so the sums are: 7, 7+1, 7+1+8,
7+1+8+2,... = 7,8,16,18,...

Crossrefs

Cf. A046975 for version of this sequence including the initial 2 of e. A039918 and A046974 for analogous sequences for Pi.

Formula

a(n)=A046975(n+1)-2

A099536 Sum of the first n digits of Zeta(3) (Apery's constant), including the initial 1.

Original entry on oeis.org

1, 3, 3, 5, 5, 10, 16, 25, 25, 28, 29, 34, 43, 48, 57, 61, 63, 71, 76, 79, 88, 97, 104, 107, 115, 116, 122, 123, 128, 129, 130, 134, 138, 147, 156, 165, 165, 172, 178, 182, 191, 199, 205, 207, 216, 218, 221, 225, 225, 229, 238, 246, 254, 262, 263, 270, 279, 281
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 22 2004

Keywords

Examples

			Zeta(3)=1.20205690... so sequence begins 1, 1+2, 1+2+0, 1+2+0+2, 1+2+0+2+0,
1+2+0+2+0+5,... which gives 1, 3, 3, 5, 5, 10, ...

Links

Crossrefs

Analogous sequences for other constants: A096535 (log 2), A099534 and A046975 (e), A039918 and A046974 (Pi).
Apéry's number or Apéry's constant zeta(3) is A002117. - N. J. A. Sloane, Jul 11 2023

Programs

  • Mathematica
    Accumulate[RealDigits[Zeta[3],10,120][[1]]] (* Harvey P. Dale, Jan 18 2012 *)

A099535 Sum of the first n decimal places of log(2).

Original entry on oeis.org

6, 15, 18, 19, 23, 30, 31, 39, 39, 44, 49, 58, 67, 71, 76, 79, 79, 88, 92, 93, 100, 102, 105, 107, 108, 110, 111, 115, 120, 128, 129, 136, 142, 147, 153, 161, 161, 168, 173, 178, 178, 178, 179, 182, 186, 189, 195, 195, 197, 202, 207, 209, 214, 218, 219, 221, 221
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 22 2004

Keywords

Examples

			log(2) decimals = 693147180559945... so the sums are 6, 6+9, 6+9+3, 6+9+3+1,... which are 6, 15, 18, 19, ...

Crossrefs

Cf. A039918 and A046974 for Pi, A046975 and A099534 for e.

Programs

  • Mathematica
    Accumulate[RealDigits[Log[2],10,100][[1]]]  (* Harvey P. Dale, Mar 23 2011 *)

A099538 Sum of the first n digits of sqrt(2), including the initial "1".

Original entry on oeis.org

1, 5, 6, 10, 12, 13, 16, 21, 27, 29, 32, 39, 42, 42, 51, 56, 56, 60, 68, 76, 76, 77, 83, 91, 99, 106, 108, 112, 114, 114, 123, 129, 138, 146, 146, 153, 161, 166, 172, 181, 187, 194, 195, 203, 210, 215, 218, 225, 231, 240, 244, 252, 252, 259, 262, 263, 270, 276, 282
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 22 2004

Keywords

Examples

			sqrt(2)=1.41421356237... so the sums are 1, 1+4, 1+4+1, 1+4+1+4, 1+4+1+4+2,...
which gives 1, 5, 6, 10, 12,...

Links

Crossrefs

Cf. A002193 for digits of sqrt(2). Other sequences like this one for other constants: A099534-A099537, A039918, A046974, A046975.

Programs

  • Mathematica
    Accumulate[RealDigits[Sqrt[2],10,60][[1]]] (* Harvey P. Dale, May 30 2012 *)

A099539 Sum of the first n decimal places of sqrt(2).

Original entry on oeis.org

4, 5, 9, 11, 12, 15, 20, 26, 28, 31, 38, 41, 41, 50, 55, 55, 59, 67, 75, 75, 76, 82, 90, 98, 105, 107, 111, 113, 113, 122, 128, 137, 145, 145, 152, 160, 165, 171, 180, 186, 193, 194, 202, 209, 214, 217, 224, 230, 239, 243, 251, 251, 258, 261, 262, 269, 275, 281
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 22 2004

Keywords

Comments

Cf. A099538 for a version of this sequence resulting from including all digits of sqrt(2) and not just the digits after the decimal point.

Examples

			Decimal places of sqrt(2) are 41421356237... so sums are 4, 4+1, 4+1+4, 4+1+4+2,... which gives 4, 5, 9, 11, ...

Links

Crossrefs

Cf. A099538 and A099534, A099535, A099536, A099537, A039918, A046974, A046975 for analogous sequences based on other constants.

Programs

  • Mathematica
    Accumulate[Rest[RealDigits[N[Sqrt[2],70]][[1]]]] (* Harvey P. Dale, Dec 12 2010 *)

Formula

a(n) = A099538(n+1) - 1.

A099540 Sum of the first n digits of log(Pi)=1.14472988584940017...

Original entry on oeis.org

1, 2, 6, 10, 17, 19, 28, 36, 44, 49, 57, 61, 70, 74, 74, 74, 75, 82, 86, 87, 91, 94, 98, 100, 107, 110, 115, 116, 119, 124, 127, 127, 132, 140, 147, 148, 149, 155, 159, 166, 168, 177, 181, 189, 190, 192, 201, 202, 207, 210, 211, 212, 217, 224, 225, 230, 231, 234
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 25 2004

Keywords

Examples

			log(Pi)=1.14472988584940017... which gives the sums 1, 1+1, 1+1+4, 1+1+4+4, 1+1+4+4+7,... leading to the terms 1, 2, 6, 10, 17,...

Crossrefs

Similarly constructed sequences A099534-A099539, A093084, A039918, A046974, A046975. Digits of log(Pi)=A053510.

Programs

  • Mathematica
    Accumulate[RealDigits[Log[Pi],10,120][[1]]] (* Harvey P. Dale, Aug 14 2018 *)

A131660 Positions at which the sum of the digits of e up to that point equals the sum of the digits of Pi up to that point.

Original entry on oeis.org

218, 241, 264, 269, 280, 287, 354, 1159, 1836, 1871, 1872, 1886, 1891, 1892, 1914, 5023, 5026, 5039, 9165, 9170, 9171, 9180, 15166, 17909, 91192, 91194, 91277, 91289, 91290, 91293, 92029, 92031, 92033, 92038, 93913, 93927, 93928, 97369, 97839
Offset: 1

Views

Author

Sergio Pimentel, Sep 13 2007

Keywords

Comments

Numbers n such that A046974(n) = A046975(n). - Robert G. Wilson v, Sep 16 2007

Examples

			a(1)=218 because the sum of the first 218 digits of e (including the initial 2) equals 987. That is the same result for the first 218 digits of Pi (including the initial 3).

Links

Crossrefs

Cf. A000796, A001113.

Programs

  • Mathematica
    de = First@ RealDigits[E, 10, 10^5]; dse = 0; dpi = First@ RealDigits[Pi, 10, 10^5]; dspi = 0; lst = {}; Do[ dse = dse + de[[n]]; dspi = dspi + dpi[[n]]; If[dse == dspi, AppendTo[lst, n]; Print@n], {n, 10^5}] (* Robert G. Wilson v, Sep 16 2007 *)
Module[{nn=100000,ed,pd},ed=Accumulate[RealDigits[E,10,nn][[1]]];pd= Accumulate[ RealDigits[Pi,10,nn][[1]]];Flatten[Position[Thread[ {ed,pd}], ?(#[[1]]==#[[2]]&),{1},Heads->False]]] (* _Harvey P. Dale, Feb 18 2015 *)

Extensions

More terms from Robert G. Wilson v, Sep 16 2007
a(6) corrected by N. J. A. Sloane, Nov 23 2007

A180231 Prime partial sums of digits of decimal expansion of e.

Original entry on oeis.org

2, 29, 37, 47, 79, 103, 173, 191, 257, 269, 331, 491, 523, 547, 547, 547, 641, 673, 677, 701, 701, 739, 751, 797, 823, 853, 881, 907, 907, 919, 977, 977, 1013, 1039, 1051, 1063, 1091, 1093, 1097, 1153, 1163, 1201, 1213, 1237, 1259, 1279, 1373, 1427, 1427, 1433, 1487
Offset: 1

Views

Author

Jason G. Wurtzel, Aug 18 2010

Keywords

Crossrefs

A046975 INTERSECT A000040.

Programs

  • Mathematica
    Select[Accumulate[First[RealDigits[N[E,500]]]],PrimeQ] (* Harvey P. Dale, Aug 19 2010 *)

Extensions

More terms from Harvey P. Dale, Aug 19 2010
Further terms from R. J. Mathar, Aug 20 2010

A387472 Numbers k such that the sum of the first k digits of e is divisible by k.

Original entry on oeis.org

1, 5, 13, 87
Offset: 1

Views

Author

Harvey P. Dale, Aug 30 2025

Keywords

Comments

For large n, A046975(n-1)/n is very close to 4.5, so is never an integer. - Alois P. Heinz, Sep 02 2025

Examples

			5 is a term since 2+7+1+8+2 = 20 is divisible by 5.

Crossrefs

Cf. A001113, A046975, A098934.

Programs

  • Mathematica
    Module[{nn=20000,ed},ed=RealDigits[E,10,nn][[1]];Select[Range[nn],Mod[Total[Take[ed,#]],#]==0&]]

Formula

{k such that k divides A046975(k-1)}. - Michael S. Branicky, Aug 30 2025
Showing 1-9 of 9 results.

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

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