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 1-6 of 6 results.

A013919 Numbers n such that sum of first n composites is composite.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 38, 39, 40, 41, 42, 44, 45, 46, 49, 50, 51, 52, 55, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 69, 70, 71, 72, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93
Offset: 1

Views

Author

N. J. A. Sloane, Henri Lifchitz

Keywords

Links

Crossrefs

Cf. A013920, A013921.

Programs

  • Mathematica
    f[ n_Integer ] := Block[ {k = n + PrimePi[ n ] + 1}, While[ k - PrimePi[ k ] - 1 != n, k++ ]; k ]; s = 0; Do[ s = s + f[ n ]; If[ ! PrimeQ[ s ], Print[ n ] ], {n, 1, 100} ]
With[{comps=Rest[Select[Range[150],!PrimeQ[#]&]]},Rest[Flatten[ Position[ Accumulate[ comps],?(!PrimeQ[#]&)]]]] (* _Harvey P. Dale, Oct 16 2013 *)

Extensions

More terms from David W. Wilson

A013920 Composite numbers k such that the sum of all composites <= k is composite.

Original entry on oeis.org

4, 6, 8, 9, 12, 14, 15, 16, 18, 20, 21, 22, 25, 26, 28, 30, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 55, 56, 57, 58, 60, 63, 64, 65, 69, 70, 72, 74, 77, 78, 80, 81, 82, 84, 85, 86, 90, 91, 92, 94, 95, 96, 98, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 118, 119
Offset: 1

Views

Author

N. J. A. Sloane, Henri Lifchitz

Keywords

Crossrefs

Cf. A013919, A013921.

Extensions

More terms from David W. Wilson

A364797 Prime powers that are equal to the sum of the first k prime powers (not including 1) for some k.

Original entry on oeis.org

2, 5, 9, 29, 49, 137, 281, 359, 449, 1579, 2029, 2281, 2677, 5519, 12527, 13229, 15451, 17047, 22409, 24389, 25931, 29191, 32687, 42937, 45757, 53239, 56443, 59743, 70201, 81677, 90863, 95087, 101627, 113111, 169343, 200407, 206911, 256049, 302977, 330133, 338707, 356263
Offset: 1

Views

Author

Ilya Gutkovskiy, Aug 08 2023

Keywords

Examples

			49 is a term because 49 is a prime power and 49 = 2 + 3 + 4 + 5 + 7 + 8 + 9 + 11.

Links

Crossrefs

Cf. A013918, A013921, A013932, A246655, A364796.

Programs

  • Mathematica
    Select[Accumulate[Select[Range[2250], PrimePowerQ]], PrimePowerQ]
  • PARI
    list(lim) = {my(s = 0); for(p = 1, lim, if(isprimepower(p), s += p; if(isprimepower(s), print1(s, ", "))));} \\ Amiram Eldar, Jun 20 2025

A364947 Prime powers that are equal to the sum of the first k prime powers (including 1) for some k.

Original entry on oeis.org

1, 3, 79, 163, 499, 947, 1279, 5297, 6689, 9629, 10853, 17467, 21001, 23887, 25411, 29761, 32089, 33289, 47947, 49429, 55633, 80687, 84697, 96157, 116719, 119159, 126641, 131783, 136991, 153371, 156227, 167861, 182969, 215249, 243161, 257921, 280897, 288853
Offset: 1

Views

Author

Ilya Gutkovskiy, Aug 14 2023

Keywords

Examples

			79 is a term because 79 is a prime power and 79 = 1 + 2 + 3 + 4 + 5 + 7 + 8 + 9 + 11 + 13 + 16 = 1 + 2 + 3 + 2^2 + 5 + 7 + 2^3 + 3^2 + 11 + 13 + 2^4.

Links

Crossrefs

Intersection of A000961 and A024918.
Cf. A013918, A013921, A013932, A364797

Programs

  • Mathematica
    Select[Accumulate[Select[Range[2000], # == 1 || PrimePowerQ[#] &]], # == 1 || PrimePowerQ[#] &]
  • PARI
    isp(n) = n == 1 || isprimepower(n);
list(lim) = {my(s = 0); for(p = 1, lim, if(isp(p), s += p; if(isp(s), print1(s, ", "))));} \\ Amiram Eldar, Jun 20 2025

A020642 n-th composite is sum of first k composites for some k.

Original entry on oeis.org

1, 5, 10, 17, 33, 44, 56, 69, 82, 99, 116, 134, 175, 196, 242, 267, 321, 349, 377, 408, 442, 475, 507, 542, 581, 619, 659, 700, 741, 785, 966, 1015, 1065, 1111, 1167, 1273, 1329, 1383, 1563, 1622, 1687, 1751, 1949, 2017, 2084, 2159, 2231, 2302, 2375, 2449, 2685
Offset: 1

Views

Author

N. J. A. Sloane, Henri Lifchitz, David W. Wilson

Keywords

Crossrefs

Cf. A013919, A013920, A013921.

A364948 Perfect powers that are equal to the sum of the first k perfect powers > 1 for some k.

Original entry on oeis.org

4, 121, 2548735225
Offset: 1

Views

Author

Ilya Gutkovskiy, Aug 14 2023

Keywords

Examples

			121 is a term because 121 = 11^2 = 4 + 8 + 9 + 16 + 25 + 27 + 32 = 2^2 + 2^3 + 3^2 + 2^4 + 5^2 + 3^3 + 2^5.

Crossrefs

Cf. A001597, A013918, A013921, A013932.

Programs

  • Mathematica
    Select[Accumulate[Select[Range[3723875], GCD @@ FactorInteger[#][[All, 2]] > 1 &]], GCD @@ FactorInteger[#][[All, 2]] > 1 &]
Showing 1-6 of 6 results.

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

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