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 1-3 of 3 results.

A222592 Smallest integer that is a sum of 2*k consecutive primes for each k = 1..n.

Original entry on oeis.org

5, 36, 8412, 227304, 39851304, 1622295444, 55789710106764
Offset: 1

Views

Author

Zak Seidov, Feb 26 2013

Keywords

Examples

			a(1) = 5 = 2+3;
a(2) = 36 = 17+19 = 5+7+11+13;
a(3) = 8412 = 4201 + 4211 =
  2089 + 2099 + 2111 + 2113 =
  1373 + 1381 + 1399 + 1409 + 1423 + 1427;
a(4) = 227304 = 113647 + 113657 =
  56813 +  56821 + 56827 + 56843 =
  37861 + 37871 + 37879 + 37889 + 37897 + 37907 =
  28387 + 28393 + 28403 + 28409 +
  28411 + 28429 + 28433 + 28439;
a(5) = 39851304 = 19925627 + 19925677 =
  9962809 + 9962819 + 9962837 + 9962839 =
  6641839 + 6641851 + 6641867 + 6641891 + 6641903 + 6641953 =
  4981367 + 4981373 + 4981387 + 4981393 +
  4981423 + 4981441 + 4981451 + 4981469 =
  3985063 + 3985067 + 3985073 + 3985087 + 3985099 +
  3985103 + 3985181 + 3985207 + 3985211 + 3985213.
The initial primes of the 6 tuples corresponding to a(6) are 811147721, 405573827, 270382529, 202786813, 162229471, and 135191207. - _Giovanni Resta_, Feb 26 2013

Crossrefs

Cf. A222564, A288340.

Programs

  • Mathematica
    a[n_] := Block[{t, w}, t = Table[{Total@(w = Prime@Range@(2*i)), w}, {i, n}]; While[Length@Union[First /@ t] > 1, t = Sort@t; w = NextPrime@t[[1,2,-1]]; t[[1,1]] += w - t[[1,2,1]]; t[[1,2]] = Append[Rest@t[[1,2]], w]]; t[[1,1]]]; Array[a,4] (* Giovanni Resta, Feb 26 2013 *)

Extensions

a(6) from Giovanni Resta, Feb 26 2013
a(7) from Max Alekseyev, Feb 12 2023

A305546 Primes that are sums of three, five, seven and eleven consecutive primes.

Original entry on oeis.org

311, 67141, 125963951, 161888809, 201388259, 559069591, 669472577, 917135831, 951993491, 974896207, 1103919101, 1128722657, 1426246369, 1691534683, 1977185207, 2455167607, 2472527851, 2558204381, 2583232213, 2643398713, 2708464399, 2815245317, 2868455287
Offset: 1

Views

Author

Zak Seidov, Jun 04 2018

Keywords

Comments

Intersection of A127340 and A213814.
E.g., a(1) = 311 = A127340(3) = A213814(1).

Links

Crossrefs

Cf. A127340, A213814, A222564.

Programs

  • Mathematica
    Module[{nn=10^8,prs,p3,p5,p7,p11},prs=Prime[Range[nn]];p3=Select[ Total/@ Partition[ prs,3,1],PrimeQ];p5=Select[Total/@Partition[prs,5,1],PrimeQ];p7=Select[ Total/@Partition[prs,7,1],PrimeQ];p11=Select[Total/@Partition[prs,11,1],PrimeQ];Intersection[ p3,p5,p7,p11]] (* Harvey P. Dale, Sep 05 2022 *)

Extensions

a(7)-a(23) from Giovanni Resta, Jun 07 2018

A360698 Smallest number that is a sum of 2*k+1 consecutive prime numbers for each k in {1, 2, ..., n}.

Original entry on oeis.org

10, 83, 311, 400861, 656303169, 460787266801, 108315769373443
Offset: 1

Views

Author

Max Alekseyev, Feb 16 2023

Keywords

Comments

a(n) <= A222564(n+1), where the equality holds whenever a(n) is prime.
Except for a(1) = 10 = 2 + 3 + 5, the terms are odd and formed by sums of odd primes.

Crossrefs

Cf. A222564, A222592, A288340.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.