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.

Previous Showing 11-17 of 17 results.

A211170 Primes that are sum of both three and five consecutive primes.

Original entry on oeis.org

83, 199, 311, 941, 1151, 1381, 2357, 3121, 4337, 4363, 4957, 5059, 7039, 8069, 8117, 8161, 8389, 8627, 8819, 8971, 9011, 9349, 10211, 10253, 13127, 14813, 16249, 19207, 19717, 21377, 23143, 24329, 32983, 34807, 38113, 39623, 41141, 44279, 45061, 45979, 58403
Offset: 1

Views

Author

Zak Seidov, Jan 31 2013

Keywords

Comments

Intersection of A034962 and A034965.

Examples

			a(1) = 83 = A034962(6) = 23 + 29 + 31 = A034965(3) = 11 + 13 + 17 + 19 + 23.

Links

Crossrefs

Cf. A034962, A034965, A073681, A152468.

Programs

  • Mathematica
    Module[{prs=Prime[Range[3000]],pr3,pr5},pr3=Select[Total/@Partition[ prs, 3, 1], PrimeQ];pr5=Select[Total/@Partition[prs,5,1],PrimeQ];Intersection[ pr3,pr5]] (* Harvey P. Dale, Oct 24 2016 *)

A298763 Numbers that are the smallest of four consecutive primes, no three of which sum to a nonprime.

Original entry on oeis.org

19, 29, 1303, 3119, 4933, 6353, 7841, 10859, 13933, 24749, 26513, 28603, 31069, 33487, 38609, 43067, 52387, 53731, 61979, 78031, 91781, 93871, 97561, 102929, 108127, 112403, 113341, 114599, 141937, 144967, 151883, 151969, 192883, 224909, 267961, 270371, 270577, 270763, 281531, 282959, 285979
Offset: 1

Views

Author

Hans Havermann, Jan 26 2018

Keywords

Examples

			19, 23, 29, 31 are four consecutive primes. The four ways of adding three of them yields 71, 73, 79, 83, all of which are prime. So 19 is a term of the sequence.

Links

Crossrefs

Subsequence of A073681.

Programs

  • Mathematica
    s={2,3,5,7}; p=s[[-1]]; While[p<10^6, If[PrimeQ[s[[1]]+s[[2]]+s[[3]]]&&PrimeQ[s[[1]]+s[[2]]+s[[4]]]&&PrimeQ[s[[1]]+s[[3]]+s[[4]]]&&PrimeQ[s[[2]]+s[[3]]+s[[4]]], Print[s[[1]]]]; p=NextPrime[p]; s=Join[Rest[s],{p}]]

A174742 Smallest of three consecutive primes whose sum is not a prime.

Original entry on oeis.org

2, 3, 13, 37, 43, 47, 59, 73, 89, 97, 103, 107, 113, 127, 131, 137, 151, 167, 173, 179, 181, 191, 193, 199, 223, 227, 233, 239, 241, 251, 257, 263, 269, 277, 307, 313, 317, 331, 353, 359, 367, 373, 383, 397, 419, 421, 433, 439, 443, 461, 479, 487, 503, 521, 523, 541, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613
Offset: 1

Views

Author

Robert Wintner, Nov 30 2010

Keywords

Crossrefs

Cf. A073681.

Programs

  • Magma
    [NthPrime(n): n in [1..150] | not IsPrime(NthPrime(n) + NthPrime(n+1) + NthPrime(n+2))]; // Vincenzo Librandi Mar 16 2020
  • Mathematica
    Prime[Select[Range[1000], ! PrimeQ[Prime[#] + Prime[# + 1] + Prime[# + 2]] &]]
Transpose[Select[Partition[Prime[Range[200]],3,1],!PrimeQ[ Total[#]]&]] [[1]] (* Harvey P. Dale, Jun 04 2013 *)

Formula

A000040 \ A073681.

A288041 Numbers k such that prime(k) + prime(k+1) + ... + prime(k+4) is prime.

Original entry on oeis.org

3, 4, 5, 6, 8, 10, 11, 14, 16, 17, 19, 21, 22, 28, 29, 30, 31, 33, 35, 36, 37, 38, 41, 43, 47, 48, 50, 56, 57, 63, 64, 70, 71, 72, 75, 76, 79, 80, 81, 84, 86, 87, 89, 91, 92, 98, 99, 100, 102, 104, 105, 106, 109, 112, 114, 119, 123, 125, 134, 140, 141, 142, 146, 148, 149, 150
Offset: 1

Views

Author

Zak Seidov, Jun 04 2017

Keywords

Links

Crossrefs

Cf. A000720 (PrimePi), A072225 (numbers n such that prime(n) + prime(n+1) + prime(n+2) is prime), A073681 (smallest of three consecutive primes whose sum is a prime), A152468 (smallest of five consecutive primes whose sum is a prime).

Programs

  • Mathematica
    With[{nn = 154}, Function[s, Select[Range[nn - 4], PrimeQ@ Total@ Take[s, {#, # + 4}] &]]@ Prime@ Range@ nn] (* Michael De Vlieger, Jun 06 2017 *)
Position[Total/@Partition[Prime[Range[200]],5,1],?(PrimeQ[#]&)]//Flatten (* _Harvey P. Dale, Sep 09 2024 *)
  • PARI
    list(lim)=my(v=List(),u=primes(5),n=1); forprime(p=13,, if(n++>lim, break); u=concat(u[2..5],p); if(isprime(vecsum(u)), listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Jun 10 2017

Formula

a(n) = pi(A152468(n)) = A000720(A152468(n)).

A220569 Smallest prime divisor of prime(n) + prime(n+1) + prime(n+2).

Original entry on oeis.org

2, 3, 23, 31, 41, 7, 59, 71, 83, 97, 109, 11, 131, 11, 3, 173, 11, 199, 211, 223, 5, 251, 269, 7, 7, 311, 11, 7, 349, 7, 5, 11, 5, 439, 457, 3, 487, 503, 3, 13, 19, 5, 7, 19, 607, 3, 661, 7, 13, 701, 23, 17, 7, 3, 3, 11, 19, 829, 29, 857, 883, 911, 7, 941
Offset: 1

Views

Author

Zak Seidov, Dec 16 2012

Keywords

Examples

			a(6) = 7 because prime(6) + prime(6+1) + prime(6+2) = 13 + 17 + 19 = 49 and the smallest prime factor of 49 is 7.

Links

Crossrefs

Cf. A034961, A034962, A073681.

Programs

  • PARI
    {a=2; b=3; c=5; for(n=1, 100, s=a+b+c;
dv=divisors(s); print1(dv[2]", "); a=b; b=c; c=nextprime(c+2))}

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]]

A117714 a(n) = (A034962(n) - A152470(n))/2.

Original entry on oeis.org

6, 9, 12, 18, 21, 26, 30, 34, 42, 56, 64, 69, 72, 81, 86, 102, 111, 144, 150, 160, 165, 198, 217, 231, 274, 282, 288, 300, 312, 342, 348, 351, 381, 393, 405, 414, 432, 453, 459, 465, 473, 495, 501, 515
Offset: 1

Views

Author

Roger L. Bagula, Apr 13 2006

Keywords

Comments

The sequence is always increasing.

Crossrefs

Cf. A072225, A073681.

Programs

  • Mathematica
    a = Flatten[Table[If[PrimeQ[Prime[n] + Prime[n + 1] + Prime[n + 2]] == True, If [Prime[n] + Prime[n + 1] + Prime[n + 2] - Prime[m] == 0, {( Prime[m] - Prime[n + 2])/2}, {}], {}], {n, 1, 100}, {m, 1, 500}]]

Extensions

Description simplified by the Assoc. Eds. of the OEIS, Jun 27 2010
Previous Showing 11-17 of 17 results.

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