A046974 -id:A046974 - cp's OEIS frontend

A059582 First differences give digits of Pi = 3.1415926...

1, 4, 5, 9, 10, 15, 24, 26, 32, 37, 40, 45, 53, 62, 69, 78, 81, 83, 86, 94, 98, 104, 106, 112, 116, 119, 122, 130, 133, 135, 142, 151, 156, 156, 158, 166, 174, 178, 179, 188, 195, 196, 202, 211, 214, 223, 232, 235, 242, 247, 248, 248, 253, 261, 263, 263, 272

Offset: 0

Rodolfo Kurchan, Feb 17 2001

A more natural variant is given by A046974, the partial sums of the digits of Pi (A000796). Maybe the present version is motivated by the coincidence that the first four digits 1,4,5,9 are similar to the decimals .14159 of Pi. - M. F. Hasler, Jan 19 2015

Harry J. Smith, Table of n, a(n) for n = 0..2000
A. Frank & P. Jacqueroux, International Contest, 2001. Item 14

Cf. A253906, A253907.

Digits := 200: it := evalf(Pi, 200)/10: out := 1: for i from 1 to 200 do printf(`%d,`,out): out := out+floor(10*it): it := 10*it-floor(10*it): od:

Accumulate[Join[{1},RealDigits[Pi,10,60][[1]]]] (* Harvey P. Dale, Jan 18 2015 *)

{ default(realprecision, 2080); a=1; x=Pi/10; for (n=0, 2000, d=floor(x); x=(x-d)*10; write("b059582.txt", n, " ", a+=d)); } \\ Harry J. Smith, Jun 28 2009

More terms from James Sellers, Feb 19 2001

A098934 Numbers n such that the sum of the first n digits of Pi are divisible by n.

Original entry on oeis.org

1, 2, 9, 11, 16

Offset: 1

Anne M. Donovan (anned3005(AT)aol.com), Oct 20 2004

For large n, A046974(n-1)/n is very close to 4.5, so is never an integer. - David Wasserman, Feb 27 2008

			a[1] = 1 since 3 is divisible by 1.
a[2] = 2 since 3 + 1 = 4 is divisible by 2.
a[3] != 3 since 3 + 1 + 4 = 8 is not divisible by 3.

Cf. A046974.

$MaxPrecision = 2500000; pd = RealDigits[N[Pi, 2000000]][[1]]; s = 0; Do[s = s + pd[[n]]; If[ Mod[s, n] == 0, Print[n]], {n, 2000000}] (* Robert G. Wilson v, Oct 21 2004 *)
Module[{nn=20,pid},pid=RealDigits[Pi,10,nn][[1]];Select[Range[nn],Mod[Total[Take[pid,#]],#]==0&]] (* Harvey P. Dale, Aug 30 2025 *)

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

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

			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,...

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

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

Sergio Pimentel, Sep 13 2007

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

			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).

Robert G. Wilson v, Table of n, a(n) for n = 1..4105.
Eric Weisstein's World of Mathematics, e.
Eric Weisstein's World of Mathematics, PI.

Cf. A000796, A001113.

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 *)

More terms from Robert G. Wilson v, Sep 16 2007

a(6) corrected by N. J. A. Sloane, Nov 23 2007

A133213 Prime partial sums of digits of decimal expansion of pi (A000796).

Original entry on oeis.org

3, 23, 31, 61, 97, 103, 157, 173, 241, 271, 313, 421, 433, 443, 449, 491, 503, 503, 523, 541, 541, 547, 557, 607, 617, 617, 647, 673, 673, 733, 757, 773, 787, 811, 821, 823, 887, 907, 911, 929, 977, 983, 991, 997, 1019, 1103, 1123, 1123, 1171, 1201, 1201

Offset: 1

Lekraj Beedassy, Dec 29 2007

Prime terms of A046974.

Cf. A000796, A046974, A180231.

Select[Accumulate[First[RealDigits[N[ \[Pi],500]]]],PrimeQ] [Harvey Dale]

Terms a(10)-a(16) added by Jason G. Wurtzel, Aug 18 2010

Further terms from Harvey P. Dale, Aug 21 2010

A276111 Decimal expansion of Pi truncated to numbers such that the partial sums of the decimal digits are perfect squares.

Original entry on oeis.org

31, 3141, 3141592, 314159265, 31415926535897932384626433

Offset: 1

Michel Lagneau, Aug 18 2016

Members of A011545.
a(6)= 3141592653...647093 contains 123 digits;
a(7)= 3141592653...128475 contains  226 digits;
a(8)= 3141592653...786783 contains 238 digits;
a(9)= 3141592653...789259 contains 357 digits;
a(10)= 3141592653...892590 contains 358 digits;
a(11)= 3141592653...261179 contains 441 digits.
The corresponding partial sums are 4, 9, 25, 36, 121,...(subsequence of A046974).
The corresponding square roots are in the following sequence b(n): 2, 3, 5, 6, 11, 24, 32, 33, 40, 44, 52, 62, 65, 66, 89, 100, 101, 110, 115, 116, 121, 135, 142, 144, 159, 161, 173, 177, 187, 190, 196, 197,...
The primes in b(n) are 2, 3, 5, 11, 89, 101, 173, 197, 227,...
The squares in b(n) are 100, 121, 144, 196, 256, 289, 324, 729, 784,..

Harvey P. Dale, Table of n, a(n) for n = 1..17

Cf. A000796, A011545, A046974.

L=Rest@FoldList[Plus,0,First@RealDigits[Pi,10,500]];Do[If[IntegerQ[Sqrt[L[[n]]]],Print[FromDigits[First@RealDigits[Pi,10,n]]]],{n,500}]
Module[{nn=50,pid,ac,po},pid=RealDigits[Pi,10,nn][[1]];ac=Accumulate[pid];po=Flatten[Position[ac,?(IntegerQ[Sqrt[#]]&)]];FromDigits/@ Table[ Take[ pid,k],{k,po}]] (* _Harvey P. Dale, May 24 2019 *)

A076819 Least position m > n in the decimal expansion of Pi=3.1415... such that the sum of all digits at positions < n is not greater than the sum of all digits at positions > n and <= m.

Original entry on oeis.org

3, 5, 6, 6, 10, 12, 13, 14, 15, 18, 20, 24, 27, 31, 34, 35, 36, 38, 40, 42, 43, 45, 46, 47, 48, 52, 54, 56, 57, 59, 63, 63, 63, 67, 70, 73, 75, 76, 80, 81, 82, 85, 88, 90, 97, 100, 101, 102, 105, 105, 106, 109, 110, 112, 114, 119, 121, 123, 126, 128, 130, 132, 135

Offset: 2

Reinhard Zumkeller, Nov 17 2002

For n > 1: A046974(n-1) <= A046974(a(n)) - A046974(n) and A046974(n-1) > A046974(a(n)-1) - A046974(n).

			n=6: 3+1+4+1+5 <= 2+6+5+3 and 3+1+4+1+5 > 2+6+5; '31415[9]26535897...'.

Cf. A000796.

A306389 Partial sums of (k-th digit of decimal expansion of Pi multiplied by (-1)^k).

Original entry on oeis.org

-3, -2, -6, -5, -10, -1, -3, 3, -2, 1, -4, 4, -5, 2, -7, -4, -6, -3, -11, -7, -13, -11, -17, -13, -16, -13, -21, -18, -20, -13, -22, -17, -17, -15, -23, -15, -19, -18, -27, -20, -21, -15, -24, -21, -30, -21, -24, -17, -22, -21, -21, -16, -24, -22, -22, -13, -20, -16, -25, -21, -25, -20, -29, -27, -30, -30, -37, -29, -30, -24, -28

Offset: 1

Luca Petrone, Feb 12 2019

a(n) > 0 for n = 8, 10, 12, 14, 16124, 16126, ... and a(n) = 0 for n = 16120, 16161, 16937, ... - Michel Marcus, Feb 13 2019

Cf. A000796, A046974, A099816, A099817.

Accumulate@ MapIndexed[(-1)^First[#2]*#1 &, First@ RealDigits[Pi, 10, 71]] (* Michael De Vlieger, Feb 15 2019 *)

a(n) = Sum_{k=1..n} (-1)^k*A000796(k).

a(n) = Sum_{k=1..floor(n/2)} A099817(k) - Sum_{k=1..floor((n+1)/2)} A099816(k). - Michel Marcus, Feb 16 2019

cp's OEIS Frontend

A059582 First differences give digits of Pi = 3.1415926...

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions

A098934 Numbers n such that the sum of the first n digits of Pi are divisible by n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A133213 Prime partial sums of digits of decimal expansion of pi (A000796).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Extensions

A276111 Decimal expansion of Pi truncated to numbers such that the partial sums of the decimal digits are perfect squares.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A076819 Least position m > n in the decimal expansion of Pi=3.1415... such that the sum of all digits at positions < n is not greater than the sum of all digits at positions > n and <= m.

Views

Author

Keywords

Comments

Examples

Crossrefs

A306389 Partial sums of (k-th digit of decimal expansion of Pi multiplied by (-1)^k).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula