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.

A364694 Polygonal numbers of order greater than 2 (A090466) which are the sum of the first k primes, for some k > 0.

Original entry on oeis.org

10, 28, 58, 100, 129, 160, 238, 328, 381, 501, 568, 639, 712, 874, 963, 1060, 1161, 1264, 1371, 1480, 1593, 1720, 1851, 2127, 2276, 2427, 2584, 2914, 3087, 3447, 3831, 4227, 4438, 4888, 5350, 5589, 5830, 6081, 6601, 6870, 8275, 10191, 10887, 11599, 12339, 12718
Offset: 1

Views

Author

Paolo Xausa, Aug 03 2023

Keywords

Examples

			28 is a term because it's both a triangular number and the sum of the first 5 primes (2 + 3 + 5 + 7 + 11).
58 is a term because it's both an octagonal number and the sum of the first 7 primes (2 + 3 + 5 + 7 + 11 + 13 + 17).

Links

Crossrefs

Intersection of A007504 with A090466.
Cf. A061890, A066527, A364691, A364695.

Programs

  • Mathematica
    A364693Q[n_]:=With[{d=Divisors[2n]},Catch[For[i=3,iJianing Song in A090466 *)
A364694list[kmax_]:=Select[Accumulate[Prime[Range[kmax]]],A364693Q];A364694list[100]

A364696 Nonnegative integers k such that the sum of the first k primes is a pentagonal number.

Original entry on oeis.org

0, 2, 77, 24587, 48070640, 471412484, 7471587112
Offset: 1

Views

Author

Paolo Xausa, Aug 03 2023

Keywords

Examples

			2 is a term because the sum of the first 2 primes (2 + 3 = 5) is a pentagonal number.

Links

Crossrefs

Cf. A000326, A007504, A033997, A175133, A364691, A364695, A366270.

Programs

  • Mathematica
    A364696list[kmax_]:=Module[{p=0},Join[{0},Table[If[IntegerQ[(Sqrt[24(p+=Prime[k])+1]+1)/6],k,Nothing],{k,kmax}]]];A364696list[25000] (* Paolo Xausa, Oct 06 2023 *)

Extensions

a(5) from Michel Marcus, Aug 04 2023
a(6)-a(7) from Hugo Pfoertner, Aug 04 2023

A366270 Nonnegative integers k such that the sum of the first k primes is a hexagonal number.

Original entry on oeis.org

0, 5, 93448, 39545957, 240439822, 1894541497, 132563927578
Offset: 1

Views

Author

Paolo Xausa, Oct 06 2023

Keywords

Examples

			5 is a term because the sum of the first five primes (2 + 3 + 5 + 7 + 11 = 28) is a hexagonal number.

Links

Crossrefs

Subsequence of A175133.
Cf. A000384, A007504, A033997, A364695, A364696, A366269 (corresponding hexagonal numbers).

Programs

  • Mathematica
    A366270list[kmax_]:=Module[{p=0},Join[{0},Table[If[IntegerQ[(Sqrt[8(p+=Prime[k])+1]+1)/4],k,Nothing],{k,kmax}]]];A366270list[10^5]
Showing 1-3 of 3 results.

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

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