A133013 -id:A133013 - cp's OEIS frontend

A134800 Concatenation of next n partition numbers A000041.

1, 12, 357, 11152230, 425677101135, 176231297385490627, 792100212551575195824363010, 37184565560468428349101431231014883, 179772163726015311853733844583531746326175175

Offset: 1

Omar E. Pol, Nov 12 2007

Harvey P. Dale, Table of n, a(n) for n = 1..37

Cf. A000041, A053067, A132926, A133013. See A134801 for another version.

FromDigits[Flatten[IntegerDigits/@#]]&/@With[{nn=10},TakeList[ PartitionsP[ Range[0,(nn(nn+1))/2]],Range[nn]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jul 25 2019 *)

Edited by Charles R Greathouse IV, Apr 28 2010

A134801 Concatenation of next n partition numbers of positive integers.

Original entry on oeis.org

1, 23, 5711, 15223042, 5677101135176, 231297385490627792, 1002125515751958243630103718, 456556046842834910143123101488317977, 216372601531185373384458353174632617517589134

Offset: 1

Omar E. Pol, Nov 12 2007

Harvey P. Dale, Table of n, a(n) for n = 1..37

Cf. A053067, A132926, A133013. Partition numbers: A000041. See A134800 for another version of the concatenation of next n partition numbers.

Module[{nn=10},FromDigits[Flatten[IntegerDigits/@#]]&/@TakeList[ PartitionsP[ Range[ (nn(nn+1))/2]],Range[nn]]] (* Harvey P. Dale, Apr 18 2022 *)

Edited by Charles R Greathouse IV, Apr 28 2010

A133026 Concatenation of next n Fermat numbers A000215.

Original entry on oeis.org

3, 517, 257655374294967297

Offset: 1

Omar E. Pol, Nov 09 2007

a(4) has 292 digits and is too large to include.

Amiram Eldar, Table of n, a(n) for n = 1..4

Cf. A000215, A053067, A133013.

a[n_] := FromDigits[Flatten[IntegerDigits[Table[2^(2^(k - 1)) + 1, {k, n*(n - 1)/2 + 1, n*(n + 1)/2}]]]]; Array[a, 3] (* Amiram Eldar, Jul 09 2025 *)

A133069 Successive digits of twin primes A001097.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Nov 10 2007

Also, with offset 0, decimal expansion of the constant by concatenate twin primes. Example: 0.35711131719293141435961... Hence, subsequence of A033308. - Omar E. Pol, Oct 21 2017

G. C. Greubel, Table of n, a(n) for n = 1..5000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A001097, A033308, A053067, A133013, A133014.

Flatten[IntegerDigits/@Union[Flatten[Select[Partition[Prime[ Range[ 100]],2,1], Last[#]- First[#] == 2&]]]] (* Harvey P. Dale, May 29 2014 *)

A133074 Concatenation of next n isolated primes.

Original entry on oeis.org

2, 2337, 475367, 79838997, 113127131157163, 167173211223233251, 257263277293307317331, 337353359367373379383389, 397401409439443449457467479, 487491499503509541547557563577

Offset: 1

Omar E. Pol, Nov 10 2007

Harvey P. Dale, Table of n, a(n) for n = 1..166
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A007510, A053067, A133013, A133014.

Module[{ip=Select[Prime[Range[200]],NoneTrue[#+{2,-2},PrimeQ]&],c},c = Floor[ (Sqrt[8 Length[ip]+1]-1)/2];FromDigits[Flatten[IntegerDigits/@#]]&/@TakeList[ ip,Range[c]]] (* Harvey P. Dale, Jun 09 2022 *)

A134714 Concatenation of next n Catalan numbers.

Original entry on oeis.org

1, 12, 51442, 13242914304862, 16796587862080127429002674440, 96948453535767012964479047763870017672631906564120420, 2446626702091482563640343059613650128990414732448619464014521836735307215269533550916004

Offset: 1

Omar E. Pol, Nov 12 2007

Harvey P. Dale, Table of n, a(n) for n = 1..15

Cf. A053067, A053068, A133013. Catalan numbers: A000108.

Module[{nn=50,cn},cn=CatalanNumber[Range[0,nn]];Table[ FromDigits[ Flatten[ IntegerDigits/@ Take[cn,{(n(n+1))/2+1,((n+1)(n+2))/2}]]],{n,0,Floor[ (Sqrt[ 8*nn+1]-1)/2]-1}]] (* Harvey P. Dale, May 15 2014 *)
Module[{nn=8},FromDigits[Flatten[IntegerDigits/@#]]&/@Rest[TakeList[CatalanNumber[Range[0,(nn(nn+1))/2-1]],Range[0,nn-1]]]] (* Harvey P. Dale, Oct 06 2024 *)

Edited by Charles R Greathouse IV, Apr 25 2010

A134723 Concatenation of next n odd primes.

Original entry on oeis.org

3, 57, 111317, 19232931, 3741434753, 596167717379, 838997101103107109, 113127131137139149151157, 163167173179181191193197199, 211223227229233239241251257263, 269271277281283293307311313317331

Offset: 1

Omar E. Pol, Nov 10 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Cf. A065091, A133013.

Module[{nterms=12,max},max=(nterms(nterms+1))/2+1; FromDigits[ Flatten[ IntegerDigits/@#]]&/@ With[ {pr=Prime[Range[2,max]]},Table[Take[pr, {(n(n-1))/2+1,(n(n+1))/2}],{n,nterms}]]] (* Harvey P. Dale, Nov 25 2012 *)
Module[{nn=20},FromDigits[Flatten[IntegerDigits/@#]]&/@TakeList[Prime[ Range[ 2,(nn(nn+1))/2+1]],Range[nn]]] (* Harvey P. Dale, Mar 27 2022 *)

A134733 Concatenation of next n imperfect numbers.

Original entry on oeis.org

1, 23, 457, 891011, 1213141516, 171819202122, 23242526272930, 3132333435363738, 394041424344454647, 48495051525354555657, 5859606162636465666768, 697071727374757677787980

Offset: 1

Omar E. Pol, Nov 12 2007

Harvey P. Dale, Table of n, a(n) for n = 1..200

Cf. A053067, A132943, A133013. Imperfect numbers: A132999.

Module[{nn=120,in,len},in=Select[Range[nn],DivisorSigma[1,#]!=2#&];len= Floor[x/.Last[Solve[(x(x+1))/2==Length[in]]]];FromDigits[Flatten[ IntegerDigits/@ #]]&/@TakeList[in,Range[len]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 01 2020 *)

A134794 Concatenation of next n composite numbers.

Original entry on oeis.org

4, 68, 91012, 14151618, 2021222425, 262728303233, 34353638394042, 4445464849505152, 545556575860626364, 65666869707274757677, 7880818284858687889091

Offset: 1

Omar E. Pol, Nov 26 2007

Harvey P. Dale, Table of n, a(n) for n = 1..200

Cf. A053067, A133013. Composite numbers: A002808.

cc[x_]:=FromDigits[Flatten[IntegerDigits/@x]]; Module[{nn= 100,cmps,tr,len},cmps = Select[Range[nn],CompositeQ];len=Length[cmps];tr = Floor[ (Sqrt[1+8 len]-1)/2];cc/@TakeList[cmps,Range[tr]]] (* Harvey P. Dale, Sep 26 2021 *)

A137318 Concatenation of segments of the digit sequence 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3....

Original entry on oeis.org

1, 31, 313, 1313, 13131, 313131, 3131313, 13131313, 131313131, 3131313131, 31313131313, 131313131313, 1313131313131, 31313131313131, 313131313131313, 1313131313131313, 13131313131313131, 313131313131313131

Offset: 1

Ctibor O. Zizka, Apr 06 2008

A000042 is 1,11,111,1111,11111,... concatenation of 111111111111111....
A002276 is 2,22,222,2222,22222,... concatenation of 222222222222222....
A133013 is 2,35,71113,... concatenation of 2 3 5 7 11 13 17 19 23 29,...

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

Cf. A000040, A000042.

Module[{nn=20},FromDigits/@TakeList[PadRight[{},(nn(nn+1))/2,{1,3}],Range[ nn]]] (* Harvey P. Dale, Aug 04 2021 *)

O.g.f.: x*(100x^4 + 200x^3 + 83x^2 + 20x + 1)/((10x-1)(100x^2+1)(x-1)(x^2+1)). - R. J. Mathar, Apr 09 2008

More terms from R. J. Mathar, Apr 09 2008

cp's OEIS Frontend

A134800 Concatenation of next n partition numbers A000041.

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A134801 Concatenation of next n partition numbers of positive integers.

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A133026 Concatenation of next n Fermat numbers A000215.

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A133069 Successive digits of twin primes A001097.

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A133074 Concatenation of next n isolated primes.

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A134714 Concatenation of next n Catalan numbers.

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A134723 Concatenation of next n odd primes.

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A134733 Concatenation of next n imperfect numbers.

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A134794 Concatenation of next n composite numbers.

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A137318 Concatenation of segments of the digit sequence 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3....

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