A000796 -id:A000796 - cp's OEIS frontend

A099817 Bisection of A000796 (decimal expansion of Pi).

1, 1, 9, 6, 3, 8, 7, 3, 3, 4, 2, 4, 3, 3, 7, 5, 2, 8, 1, 7, 6, 3, 9, 7, 1, 5, 2, 9, 4, 4, 5, 2, 0, 8, 6, 0, 2, 6, 0, 9, 8, 2, 0, 4, 2, 3, 2, 1, 0, 7, 8, 1, 8, 8, 5, 3, 8, 3, 6, 4, 0, 3, 4, 6, 9, 5, 5, 2, 3, 7, 5, 5, 4, 8, 2, 4, 1, 1, 4, 0, 8, 1, 2, 0, 9, 8, 2, 1, 5, 5, 6, 4, 2, 9, 8, 5, 9, 0, 8, 9, 4, 2, 8, 0, 7

Offset: 1

N. J. A. Sloane, Nov 19 2004

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

Cf. A000796, A099816.

Take[RealDigits[Pi,10,230][[1]],{2,-1,2}] (* Harvey P. Dale, Aug 11 2024 *)

More terms from Joshua Zucker, May 15 2006

A175792 a(n) = Sum_{k=1..n} (-1)^A000796(k), excess of the number of even over odd digits in the first n digits of Pi.

Original entry on oeis.org

-1, -2, -1, -2, -3, -4, -3, -2, -3, -4, -5, -4, -5, -6, -7, -8, -7, -8, -7, -6, -5, -4, -3, -2, -3, -4, -3, -4, -3, -4, -5, -6, -5, -4, -3, -2, -1, -2, -3, -4, -5, -4, -5, -6, -7, -8, -9, -10, -11, -12, -11, -12, -11, -10, -9, -10, -11, -10, -11, -10, -9, -10, -11, -10

Offset: 1

Michel Lagneau, Sep 06 2010

			a(6) = (-1)^3 + (-1)^1 + (-1)^4 + (-1)^1 + (-1)^5 + (-1)^9= -4.

cf. A000796, A030657, A196686 (negated), A175813 (indices of 0's).

Digits := 100:
A000796 := proc(n)
        floor(Pi*10^(n-1)) mod 10;
end proc:
A175792 := proc(n)
        add((-1)^A000796(k),k=1..n) ;
end proc: # R. J. Mathar, Jul 10 2012

Rest@ FoldList[ Plus, 0, (-1)^First@ RealDigits[Pi, 10, 200]]
Accumulate[Table[If[EvenQ[n],1,-1],{n,RealDigits[Pi,10,70][[1]]}]] (* Harvey P. Dale, Nov 03 2015 *)

A387193 Decimal expansion of the absolute value of J_0(Pi), Bessel Function of the first kind of index 0 at A000796.

Original entry on oeis.org

3, 0, 4, 2, 4, 2, 1, 7, 7, 6, 4, 4, 0, 9, 3, 8, 6, 4, 2, 0, 2, 0, 3, 4, 9, 1, 2, 8, 1, 7, 7, 0, 4, 9, 2, 3, 9, 6, 9, 6, 5, 0, 5, 3, 4, 7, 8, 3, 8, 9, 1, 0, 0, 3, 2, 3, 8, 2, 1, 2, 3, 4, 9, 9, 5, 8, 1, 0, 9, 4, 6, 6, 3, 2, 1, 4, 7, 5, 4, 9, 3, 4, 9, 0, 3, 7, 3, 9, 6, 4, 4, 8, 7, 3, 4, 5, 2, 3, 8, 5, 7, 1, 7, 4, 1, 7, 8, 1, 7, 0, 6, 0, 6, 9, 3, 3, 3, 9

Offset: 0

R. J. Mathar, Aug 21 2025

			J_0(Pi) = -0.30424217764409386420203491281770492396965053..

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A000796, A387194, A387195.

First[RealDigits[BesselJ[0, Pi], 10, 100]] (* Paolo Xausa, Aug 21 2025 *)

A065253 a(n) = 10*(A064823(n)-1) + A000796(n).

Original entry on oeis.org

3, 1, 4, 11, 5, 9, 2, 6, 15, 13, 25, 8, 19, 7, 29, 23, 12, 33, 18, 14, 16, 22, 26, 24, 43, 53, 28, 63, 32, 17, 39, 35, 0, 42, 38, 48, 34, 21, 49, 27, 31, 36, 59, 73, 69, 79, 83, 37, 45, 41, 10, 55, 58, 52, 20, 89, 47, 44, 99, 54, 64, 65, 109, 62, 93, 30, 57, 68, 51, 46, 74, 40

Offset: 1

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 26 2001

The sequence would be a permutation of the naturals if each of the digits 0,1,..,9 occur infinitely often in the decimal expansion of Pi. "Inverse": A065254

Cf. A064823, A000796, A065254.

a065253 n = a065253_list !! (n-1)
a065253_list = zipWith (+)
               (map ((* 10) . (subtract 1)) a064823_list) a000796_list
-- Reinhard Zumkeller, Jul 14 2013

terms = 100; Clear[cnt]; cnt[_] = n = 0;
Do[a[++n] = 10 (++cnt[k] - 1) + k, {k, RealDigits[Pi, 10, terms][[1]]}];
a /@ Range[terms] (* Jean-François Alcover, Nov 15 2019 *)

A120943 Numbers n such that merging first n digits in decimal expansion of Pi (A000796) gives a squarefree composite number.

Original entry on oeis.org

3, 5, 8, 10, 11, 12, 13, 14, 15, 16, 18, 19, 21, 22, 23, 25, 27, 28, 30, 31, 32, 34, 39, 40, 41, 43, 44, 45, 46, 48, 50, 51, 53, 54, 57, 58, 59, 60, 62, 63, 65, 66, 67, 69, 73, 76, 77, 80, 81, 82, 83, 84, 87, 88, 90, 92, 93, 94, 96, 97, 98, 99, 100, 102, 103, 104, 109, 111

Offset: 1

Zak Seidov, Aug 19 2006

Note that the indices here differ by one from those in WIFC (World Integer Factorization Center), N = int(pi*10^(n)), by Hisanori Mishima. Therefore to H. Mishima's index add one.

			n=3: first 3 digits give 314=2*157
n=5: first 5 digits give 31415=5*61*103
n=8: 31415926=2*1901*8263
n=10: 3141592653=3*107*9786893
n=11: 31415926535=5*7*31*28954771
n=12: 314159265358=2*157079632679, etc.

Dario Alejandro Alpern, Java Applet: Factorization using the Elliptic Curve Method.
H. Mishima, Factorizations of many number sequences
H. Mishima, Factorizations of many number sequences

Cf. A000796 = Decimal expansion of Pi, A011545 = Decimal expansion of pi truncated to n places.
Cf. A000796, A011545.
Complement of A120943 is A121865.

(* first do *) Needs["NumberTheory`NumberTheoryFunctions`"] (* then *) p = RealDigits[Pi, 10, 100][[1]]; fQ[n_] := Block[{fd = FromDigits@ Take[p, n]}, !PrimeQ@fd && SquareFreeQ@fd]; Select[Range@81, fQ@# &] (* Robert G. Wilson v *)
Module[{nn=120,p,c},p=RealDigits[Pi,10,nn][[1]];Select[Range[nn], CompositeQ[ c=FromDigits[Take[p,#]]]&&SquareFreeQ[c]&]] (* Harvey P. Dale, Mar 25 2015 *)

Numbers n such that A011545(n) is squarefree.

More terms from Robert G. Wilson v, Aug 21 2006

A163579 Primes of the form floor(k(k+1)Pi/2), k>=0, where Pi = 3.1415.. = A000796.

Original entry on oeis.org

3, 31, 47, 113, 659, 1021, 1187, 1979, 2971, 3251, 5749, 9679, 10433, 14627, 20593, 22807, 23957, 35107, 39461, 55813, 58207, 109063, 152417, 157349, 201881, 227419, 244463, 262121, 292469, 295187, 310357, 318793, 320209, 323053, 328777, 333103

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 31 2009

nonn

G. C. Greubel, Table of n, a(n) for n = 1..1000

s=0;lst={};Do[s+=n;p=IntegerPart[s];If[PrimeQ[p],AppendTo[lst,p]],{n,0,7!,Pi}];lst
Select[Floor[Accumulate[Range[800]]*Pi],PrimeQ] (* Harvey P. Dale, Nov 20 2018 *)

for(n=1,500, m=floor(n*(n+1)*Pi/2); if(isprime(m), print1(m, ", "))) \\ G. C. Greubel, Jul 28 2017

Definition clarified by R. J. Mathar, Sep 24 2011

A226486 First available increasing palindromes (A002113) found in the decimal expansion of Pi-3 (A000796).

Original entry on oeis.org

1, 4, 5, 9, 535, 979, 46264, 59195, 73637, 77477, 99999, 467764, 8683868, 23911932, 398989893, 559555955, 769646967, 972464279, 992868299, 21348884312, 49612121694, 450197791054, 9475082805749

Offset: 1

Patrick De Geest and Robert G. Wilson v, Jun 09 2013

Cf. A000796, A068046, A226487.

pi = RealDigits[Pi-3, 10, 2500000][[1]]; palQ[n_] := n == Reverse[n]; mx = 0; k = 1; While[k < 1000, j = 1; While[j <= k, If[ palQ[ Take[ pi, {j, k}]], p = FromDigits[ Take[ pi, {j, k}]]; If[p > mx, mx = p; Print[p]; pi = Drop[pi, k]; k = 0; Break[]]]; j++]; k++]

A349551 Rectangular array with ten rows, read by falling antidiagonals: row k gives positions of k in the decimal expansion (A000796) of Pi.

Original entry on oeis.org

33, 51, 2, 55, 4, 7, 66, 38, 17, 1, 72, 41, 22, 10, 3, 78, 50, 29, 16, 20, 5, 86, 69, 34, 18, 24, 9, 8, 98, 95, 54, 25, 37, 11, 21, 14, 107, 96, 64, 26, 58, 32, 23, 30, 12, 117, 104, 74, 28, 60, 49, 42, 40, 19, 6

Offset: 0

Clark Kimberling, Dec 17 2021

Every positive integer occurs exactly once.

It is assumed that each digit occurs infinitely many times in A000796.

			(Base-10 digits of Pi) = (3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, ...); the position of the first 0 is 33, so the first term in row 0 is 33.
Corner:
  33, 51, 55, 66, 72, 78, 86, 98,  107,  117, 122, ... A014976
   2,  4, 38, 41, 50, 69, 95, 96,  104,  111, 139, ... A053745
   7, 17, 22, 29, 34, 54, 64, 74,   77,   84,  90, ... A053746
   1, 10, 16, 18, 25, 26, 28, 44,   47,   65,  87, ... A053747
   3, 20, 24, 37, 58, 60, 61, 71,   88,   93, 105, ... A053748
   5,  9, 11, 32, 49, 52, 62, 91,  110,  131, 132, ... A053749
   8, 21, 23, 42, 70, 73, 76, 83,   99,  109, 118, ... A053750
  14, 30, 40, 48, 57, 67, 97, 100, 121,  140, 157, ... A053751
  12, 19, 27, 35, 36, 53, 68, 75,   79,   82,  85, ... A053752
   6, 13, 15, 31, 39, 43, 45, 46,   56,   59,  63, ... A053753

Index entries for sequences that are permutations of the natural numbers

Cf. A000796, A014976, A053745-A053753, A032445 (includes column 1).

r = RealDigits[Pi, 10, 200][[1]]
t = Table[Flatten[Position[r, n]], {n, 0, 9}]
TableForm[t]  (* A349551 array *)
Flatten[Table[t[[n - k + 1, k]], {n, 10}, {k, n, 1, -1}]] (* A349551 sequence *)

A110810 Binomial transform of A000796.

Original entry on oeis.org

3, 4, 9, 19, 40, 92, 220, 513, 1142, 2436, 5031, 10164, 20272, 40258, 80230, 161458, 329211, 679921, 1417373, 2966192, 6195952, 12855389, 26402016, 53574712, 107369761, 212694661, 417192840, 812167806, 1573409607, 3041468738

Offset: 0

Paul Curtz, Jun 13 2007

Vincenzo Librandi, Table of n, a(n) for n = 0..200

m:=32; R:=RealField(m); a:=Intseq(Round(Pi(R)*10^m), 10); Reverse(~a); [ &+[ Binomial(i-1, k-1)*a[k]: k in [1..i] ]: i in [1..m] ]; /* Klaus Brockhaus, Jun 15 2007 */

Edited by N. J. A. Sloane, Jun 15 2007

More terms from Klaus Brockhaus, Jun 15 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

cp's OEIS Frontend

A099817 Bisection of A000796 (decimal expansion of Pi).

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A175792 a(n) = Sum_{k=1..n} (-1)^A000796(k), excess of the number of even over odd digits in the first n digits of Pi.

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Maple

Mathematica

A387193 Decimal expansion of the absolute value of J_0(Pi), Bessel Function of the first kind of index 0 at A000796.

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Mathematica

A065253 a(n) = 10*(A064823(n)-1) + A000796(n).

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Haskell

Mathematica

A120943 Numbers n such that merging first n digits in decimal expansion of Pi (A000796) gives a squarefree composite number.

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Mathematica

Formula

Extensions

A163579 Primes of the form floor(k*(k+1)*Pi/2), k>=0, where Pi = 3.1415.. = A000796.

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Mathematica

PARI

Extensions

A226486 First available increasing palindromes (A002113) found in the decimal expansion of Pi-3 (A000796).

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Keywords

Crossrefs

Programs

Mathematica

A349551 Rectangular array with ten rows, read by falling antidiagonals: row k gives positions of k in the decimal expansion (A000796) of Pi.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A110810 Binomial transform of A000796.

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Author

Keywords

A163579 Primes of the form floor(k(k+1)Pi/2), k>=0, where Pi = 3.1415.. = A000796.