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.

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A158619 Twin prime pairs concatenated in binary representation.

Original entry on oeis.org

11101, 101111, 10111101, 1000110011, 1110111111, 101001101011, 111011111101, 10001111001001, 11001011100111, 11010111101101, 1000100110001011, 1001010110010111, 1011001110110101, 1011111111000001, 1100010111000111
Offset: 1

Views

Author

Jonathan Vos Post, Mar 22 2009

Keywords

Comments

Binary analog of A095958.

Examples

			a(1) = 11101 because 11_2 = lower of first twin prime pair = 3, and 101_2 = higher of first twin prime pair = 5.

Crossrefs

Cf. A001359, A006512, A007088, A045533, A095958.

Programs

  • Maple
    A001359 := proc(n) option remember ; if n = 1 then 3; else a := nextprime(procname(n-1)) ; while not isprime(a+2) do a := nextprime(a) ; od: RETURN(a) ; fi: end: A006512 := proc(n) A001359(n)+2 ; end: A007088 := proc(n) bdgs := convert(n,base,2) ; add( op(i,bdgs)*10^(i-1),i=1..nops(bdgs)) ; end: cat2 := proc(a,b) bdgs := max(1, 1+ilog10(b)) ; a*10^bdgs+b ; end: A158619 := proc(n) cat2(A007088(A001359(n)),A007088(A006512(n))) ; end: seq(A158619(n),n=1..30) ; # R. J. Mathar, Apr 16 2009

Formula

a(n) = A007088(A001359(n)) CONCATENATE A007088(A006512(n)) = A007088(A001359(n)) CONCATENATE A007088(A001359(n)+2).

Extensions

More terms from R. J. Mathar, Apr 16 2009

A247474 Numbers formed by concatenating two successive primes and their sum.

Original entry on oeis.org

235, 358, 5712, 71118, 111324, 131730, 171936, 192342, 232952, 293160, 313768, 374178, 414384, 434790, 4753100, 5359112, 5961120, 6167128, 6771138, 7173144, 7379152, 7983162, 8389172, 8997186, 97101198, 101103204, 103107210, 107109216, 109113222, 113127240
Offset: 1

Views

Author

Jennifer Jin, Nov 30 2014

Keywords

Comments

After the first term, every term is even.

Examples

			For n=1 the two successive primes are 2 and 3, 2+3=5. Therefore the number created is 235.

Links

Crossrefs

Cf. A001043, A045533.

Programs

  • Mathematica
    a247474[n_Integer] := Module[{p, f}, p := Prime /@ List[n, n + 1]; FromDigits@Flatten@Join[IntegerDigits[p], IntegerDigits[Plus @@ p]]]; a247474/@Range[120] (* Michael De Vlieger, Dec 01 2014 *)
FromDigits[Join[IntegerDigits[#[[1]]],IntegerDigits[#[[2]]], IntegerDigits[ Total[#]]]]&/@Partition[Prime[Range[40]],2,1] (* Harvey P. Dale, Jul 29 2015 *)

A132902 Numbers formed by concatenating 12 consecutive prime numbers.

Original entry on oeis.org

23571113171923293137, 357111317192329313741, 5711131719232931374143, 71113171923293137414347, 111317192329313741434753, 131719232931374143475359, 171923293137414347535961
Offset: 1

Views

Author

Omar E. Pol, Sep 04 2007

Keywords

Crossrefs

Prime numbers: A000040. Cf. A007795, A045533, A059932, A091762.

Programs

  • Mathematica
    FromDigits[Flatten[IntegerDigits/@#]]&/@Partition[Prime[Range[20]],12,1] (* Harvey P. Dale, May 27 2017 *)

A132904 Numbers formed by concatenating 4 consecutive prime numbers.

Original entry on oeis.org

2357, 35711, 571113, 7111317, 11131719, 13171923, 17192329, 19232931, 23293137, 29313741, 31374143, 37414347, 41434753, 43475359, 47535961, 53596167, 59616771, 61677173, 67717379, 71737983, 73798389, 79838997, 838997101
Offset: 1

Views

Author

Omar E. Pol, Sep 04 2007

Keywords

Links

Crossrefs

Prime numbers: A000040. Cf. A007795, A045533, A059932, A091762.

Formula

Prime numbers. 2 3 5 7 --------------> a(1) = 2357 11 -------------> a(2) = 35711

A132906 Numbers formed by concatenating 6 consecutive prime numbers.

Original entry on oeis.org

23571113, 357111317, 5711131719, 71113171923, 111317192329, 131719232931, 171923293137, 192329313741, 232931374143, 293137414347, 313741434753, 374143475359, 414347535961, 434753596167, 475359616771, 535961677173
Offset: 1

Views

Author

Omar E. Pol, Sep 04 2007

Keywords

Crossrefs

Prime numbers: A000040. Cf. A007795, A045533, A059932, A091762.

A132907 Numbers formed by concatenating 7 consecutive prime numbers.

Original entry on oeis.org

2357111317, 35711131719, 571113171923, 7111317192329, 11131719232931, 13171923293137, 17192329313741, 19232931374143, 23293137414347, 29313741434753, 31374143475359, 37414347535961, 41434753596167
Offset: 1

Views

Author

Omar E. Pol, Sep 04 2007

Keywords

Crossrefs

Prime numbers: A000040. Cf. A007795, A045533, A059932, A091762.

A132908 Numbers formed by concatenating 8 consecutive prime numbers.

Original entry on oeis.org

235711131719, 3571113171923, 57111317192329, 711131719232931, 1113171923293137, 1317192329313741, 1719232931374143, 1923293137414347, 2329313741434753, 2931374143475359, 3137414347535961, 3741434753596167
Offset: 1

Views

Author

Omar E. Pol, Sep 04 2007

Keywords

Crossrefs

Cf. A000040, A007795, A045533, A059932, A091762.

Programs

  • Mathematica
    FromDigits/@(Flatten[IntegerDigits/@#]&/@(Partition[Prime[Range[20]],8,1])) (* Harvey P. Dale, Mar 06 2011 *)

A132909 Numbers formed by concatenating 9 consecutive prime numbers.

Original entry on oeis.org

23571113171923, 357111317192329, 5711131719232931, 71113171923293137, 111317192329313741, 131719232931374143, 171923293137414347, 192329313741434753, 232931374143475359, 293137414347535961
Offset: 1

Views

Author

Omar E. Pol, Sep 04 2007

Keywords

Crossrefs

Prime numbers: A000040. Cf. A007795, A045533, A059932, A091762.

Programs

  • Mathematica
    FromDigits[Flatten[IntegerDigits/@#]]&/@Partition[Prime[Range[ 20]], 9, 1] (* Harvey P. Dale, Jul 18 2011 *)

A132910 Numbers formed by concatenating 10 consecutive prime numbers.

Original entry on oeis.org

2357111317192329, 35711131719232931, 571113171923293137, 7111317192329313741, 11131719232931374143, 13171923293137414347, 17192329313741434753, 19232931374143475359, 23293137414347535961
Offset: 1

Views

Author

Omar E. Pol, Sep 04 2007

Keywords

Crossrefs

Prime numbers: A000040. Cf. A007795, A045533, A059932, A091762.

A319675 Sum of digits of prime(n) and digits of prime(n+1).

Original entry on oeis.org

5, 8, 12, 9, 6, 12, 18, 15, 16, 15, 14, 15, 12, 18, 19, 22, 21, 20, 21, 18, 26, 27, 28, 33, 18, 6, 12, 18, 15, 15, 15, 16, 24, 27, 21, 20, 23, 24, 25, 28, 27, 21, 24, 30, 36, 23, 11, 18, 24, 21, 22, 21, 15, 22, 25, 28, 27, 26, 27, 24, 27, 24, 15, 12, 18, 18
Offset: 1

Views

Author

Kei Ryan, Sep 26 2018

Keywords

Examples

			For n=6 , a(6) is the sum of digits of 13 and 17 which is 12.

Crossrefs

Cf. A007605, A045533.

Programs

  • GAP
    P:=Filtered([1..400],IsPrime);; List(List([1..Size(P)-1],i->ListOfDigits(P[i])+ListOfDigits(P[i+1])),Sum); # Muniru A Asiru, Sep 26 2018
  • Magma
    [&+Intseq(NthPrime(n)) + &+Intseq(NthPrime(n+1)): n in [1..87]]; // Vincenzo Librandi, Sep 26 2018
  • Mathematica
    Table[Plus@@IntegerDigits[Prime[n]] + Plus@@IntegerDigits[Prime[n + 1]], {n, 80}] (* Vincenzo Librandi, Sep 26 2018 *)
Previous Showing 11-20 of 20 results.

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