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 1-7 of 7 results.

A073681 Smallest of three consecutive primes whose sum is a prime.

Original entry on oeis.org

5, 7, 11, 17, 19, 23, 29, 31, 41, 53, 61, 67, 71, 79, 83, 101, 109, 139, 149, 157, 163, 197, 211, 229, 271, 281, 283, 293, 311, 337, 347, 349, 379, 389, 401, 409, 431, 449, 457, 463, 467, 491, 499, 509, 547, 617, 641, 653, 659, 661, 701, 719, 743, 751, 757
Offset: 1

Views

Author

Amarnath Murthy, Aug 11 2002

Keywords

Links

Crossrefs

Cf. A152469, A152470, A174742, A034962, A152468, A180948, A189571, A180950, A226380.

Programs

  • Magma
    [NthPrime(n): n in [0..200] | IsPrime(NthPrime(n)+NthPrime(n+1)+ NthPrime(n+2))]; // Vincenzo Librandi, May 06 2015
  • Maple
    t0:=[];
t1:=[];
t2:=[];
for i from 1 to 1000 do
t3:=ithprime(i)+ithprime(i+1)+ithprime(i+2);
if isprime(t3) then
t0:=[op(t0),i];
t1:=[op(t1),ithprime(i)];
t2:=[op(t2),ithprime(i+2)];
fi;
od:
t1;
  • Mathematica
    Transpose[Select[Partition[Prime[Range[200]],3,1],PrimeQ[Total[#]]&]] [[1]] (* Harvey P. Dale, Jan 25 2012 *)
  • PARI
    forprime(p=1,1000, pp=nextprime(p+1); if(isprime(p+pp+nextprime(pp+1)),print1(p",")))
  • PARI
    A073681(n,print_all=0,start=3)={my(r,q=1);forprime(p=start,, isprime(r+(r=q)+(q=p)) & (n-- ||return(precprime(r-1))) & print_all & print1(precprime(r-1)","))} \\ M. F. Hasler, Dec 18 2012

Formula

Conjecture: for n -> oo, a(n) ~ prime(n) * (log(prime(n)))^C, where C = 8/Pi^2 (cf. A217739). - Alain Rocchelli, Sep 04 2023

Extensions

More terms from Ralf Stephan, Mar 20 2003
More cross-references from Harvey P. Dale, Jun 05 2013

A152468 Smallest of five consecutive primes whose sum is a prime.

Original entry on oeis.org

5, 7, 11, 13, 19, 29, 31, 43, 53, 59, 67, 73, 79, 107, 109, 113, 127, 137, 149, 151, 157, 163, 179, 191, 211, 223, 229, 263, 269, 307, 311, 349, 353, 359, 379, 383, 401, 409, 419, 433, 443, 449, 461, 467, 479, 521, 523, 541, 557, 569, 571, 577, 599, 613, 619
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Dec 05 2008

Keywords

Comments

Surprisingly many terms are also in A073681. - Zak Seidov, Dec 17 2012

Links

Crossrefs

Cf. A073681, A034965, A180948, A189571, A180950, A226380.

Programs

  • Mathematica
    lst={};Do[p0=Prime[n];p1=Prime[n+1];p2=Prime[n+2];p3=Prime[n+3];p4=Prime[n+4];If[PrimeQ[p=p0+p1+p2+p3+p4],AppendTo[lst,p0]],{n,6!}];lst
Transpose[Select[Partition[Prime[Range[500]], 5, 1], PrimeQ[Total[#]] &]][[1]] (* Harvey P. Dale, Jun 05 2013 *)
Prime[Select[Range[150], PrimeQ[Sum[Prime[# + i], {i, 0, 4}]] &]] (* Bruno Berselli, Aug 21 2013 *)
  • PARI
    {a=2; b=3; c=5; d=7; e=11; for(n=1,100, s=a+b+c+d+e;
if(isprime(s), print1(a", ")); a=b; b=c; c=d; d=e; e=nextprime(e+2))} /* Zak Seidov, Dec 17 2012 */

Extensions

More cross references from Harvey P. Dale, Jun 05 2013

A180948 Smallest of seven (7) consecutive primes whose sum is a prime.

Original entry on oeis.org

17, 19, 23, 29, 31, 43, 47, 53, 61, 71, 79, 89, 97, 103, 107, 113, 127, 137, 151, 233, 257, 313, 317, 359, 367, 373, 379, 383, 401, 461, 463, 487, 499, 503, 509, 521, 577, 587, 617, 619, 761, 797, 821, 827, 839, 853, 881, 883, 907, 1019, 1061, 1063, 1069, 1097
Offset: 1

Views

Author

Carmine Suriano, Sep 27 2010

Keywords

Comments

There are twins such as (17,19); (461,463); (1061,1063).
There are also consecutives such as (17,19,23,29,31); (359,367,373,379,383); (1949,1951,1973).

Examples

			a(7)=47+53+59+61+67+71+73=431 is a prime.

Links

Crossrefs

Cf. A000040, A073681, A082246, A152468, A189571, A180950, A226380.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[500]],7,1],PrimeQ[Total[#]]&]] [[1]] (* Harvey P. Dale, Jun 05 2013 *)

Extensions

More cross references from Harvey P. Dale, Jun 05 2013

A180950 Smallest prime such that the sum of successive 11 primes is a prime.

Original entry on oeis.org

5, 7, 11, 13, 19, 23, 37, 41, 59, 101, 103, 107, 109, 113, 137, 149, 151, 157, 167, 173, 191, 269, 281, 283, 293, 307, 331, 349, 353, 359, 421, 431, 463, 479, 487, 499, 503, 569, 599, 607, 613, 617, 619, 677, 733, 761, 773, 823, 853, 883, 967, 977, 1051, 1087
Offset: 1

Views

Author

Carmine Suriano, Sep 27 2010

Keywords

Comments

Sum i=0 to 10 of prime(n+i) is a prime.
There are many twins: (11,13); (149,151); (1301,1303); (1997,1999); (8969,8971) ...
There are also consecutive primes: (101,103,107,109,113); (607,613,617,619); (8681,8689,8693)

Examples

			a(5)=19 since 19+23+29+31+37+41+43+47+53+59+61=443 is a prime.

Links

Crossrefs

Cf. A000040, A127338, A073681, A152468, A180948, A189571, A226380.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[500]], 11, 1], PrimeQ[Total[#]] &]][[1]] [[1]] (* Harvey P. Dale, Jun 05 2013 *)
Prime[Select[Range[200], PrimeQ[Sum[Prime[# + i], {i, 0, 10}]] &]] (* Bruno Berselli, Aug 22 2013 *)

Extensions

More cross references from Harvey P. Dale, Jun 05 2013

A226380 Smallest of 101 consecutive primes whose sum is prime.

Original entry on oeis.org

83, 89, 139, 179, 181, 277, 281, 353, 409, 479, 499, 521, 571, 587, 643, 727, 839, 883, 887, 919, 929, 971, 977, 1019, 1021, 1117, 1213, 1223, 1237, 1259, 1303, 1327, 1367, 1381, 1399, 1423, 1433, 1481, 1483, 1667, 1723, 1789, 1823, 1861, 1879, 1913, 2083
Offset: 1

Views

Author

Harvey P. Dale, Jun 05 2013

Keywords

Links

Crossrefs

Cf. A073681, A152468, A180948, A189571, A180950.

Programs

  • Mathematica
    Transpose[Select[Partition[Prime[Range[500]],101,1],PrimeQ[Total[#]]&]] [[1]]
Prime[Select[Range[400], PrimeQ[Sum[Prime[# + i], {i, 0, 100}]] &]] (* Bruno Berselli, Aug 21 2013 *)

A228200 Smallest of 9 consecutive primes whose sum is not a prime.

Original entry on oeis.org

2, 5, 7, 11, 13, 17, 19, 23, 41, 43, 53, 59, 61, 67, 71, 73, 97, 101, 103, 113, 137, 151, 163, 167, 181, 191, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 313, 317, 331, 337, 349, 353, 379, 383, 401, 409, 419, 421, 431, 439, 443, 457, 461
Offset: 1

Views

Author

Vincenzo Librandi, Aug 20 2013

Keywords

Examples

			59 is in the sequence because 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 = 679 and 679 is not a prime.

Links

Crossrefs

Cf. A189571, A127336.

Programs

  • Magma
    [NthPrime(n): n in [1..120] |not IsPrime(&+[NthPrime(n+s): s in [0..8]])];
  • Mathematica
    Transpose[Select[Partition[Prime[Range[150]], 9, 1], !PrimeQ[Total[#]]&]][[1]]

A229059 Smallest of 13 consecutive primes whose sum is a prime.

Original entry on oeis.org

29, 41, 47, 61, 71, 89, 97, 103, 107, 131, 139, 149, 193, 211, 241, 263, 277, 293, 311, 313, 349, 353, 379, 383, 397, 401, 419, 443, 461, 491, 521, 557, 593, 599, 631, 647, 677, 739, 761, 809, 827, 877, 983, 1013, 1039, 1061, 1109, 1117, 1171, 1193, 1201
Offset: 1

Views

Author

Vincenzo Librandi, Sep 13 2013

Keywords

Examples

			a(1)=29 since 29+31+37+41+43+47+53+59+61+67+71+73+79=691 is a prime.

Links

Crossrefs

Cf. A073681, A152468, A180948, A189571, A180950, A226380.

Programs

  • Magma
    [NthPrime(n): n in [1..200] | IsPrime(&+[NthPrime(n+s): s in [0..12]])];
  • Mathematica
    Transpose[Select[Partition[Prime[Range[250]], 13, 1], PrimeQ[Total[#]]&]][[1]]
Showing 1-7 of 7 results.

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