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.

A054996 Integers that can be expressed as the sum of consecutive primes in exactly 1 way.

Original entry on oeis.org

2, 3, 7, 8, 10, 11, 12, 13, 15, 18, 19, 24, 26, 28, 29, 30, 37, 39, 42, 43, 47, 48, 49, 52, 56, 58, 61, 68, 73, 75, 77, 78, 79, 84, 88, 89, 95, 98, 102, 103, 107, 113, 121, 124, 128, 129, 132, 137, 144, 149, 150, 151, 155, 156, 157, 158, 159, 160, 161, 162, 163
Offset: 1

Views

Author

Jud McCranie, May 30 2000

Keywords

Examples

			8=3+5, so 8 is in the sequence.

References

  • R. K. Guy, Unsolved Problems in Number Theory, section C2.

Links

Crossrefs

Cf. A054845, A054859, A054997, A054998, A054999, A055000, A055001.

Formula

A054845(a(n)) = 1. - Ray Chandler, Sep 20 2023

A054999 Integers that can be expressed as the sum of consecutive primes in exactly 4 ways.

Original entry on oeis.org

1151, 1164, 1320, 1367, 1650, 1854, 1951, 2393, 2647, 2689, 2856, 2867, 3198, 3264, 3389, 3754, 4200, 4920, 4957, 5059, 5100, 5153, 5770, 5999, 6504, 7451, 7901, 8152, 8819, 10134, 10320, 10499, 10536, 10649, 10859, 10949, 11058, 12294
Offset: 1

Views

Author

Jud McCranie, May 30 2000

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, section C2.

Links

Crossrefs

Cf. A054845, A054859, A054996, A054997, A054998, A055500, A055001.

Formula

A054845(a(n)) = 4. - Ray Chandler, Sep 20 2023

A054997 Integers that can be expressed as the sum of consecutive primes in exactly 2 ways.

Original entry on oeis.org

5, 17, 23, 31, 36, 53, 59, 60, 67, 71, 72, 90, 97, 100, 101, 109, 112, 119, 120, 127, 131, 138, 139, 143, 152, 173, 180, 181, 187, 204, 210, 211, 221, 228, 233, 258, 263, 269, 271, 276, 300, 304, 323, 330, 331, 349, 353, 372, 373, 379, 384, 390, 395, 408
Offset: 1

Views

Author

Jud McCranie, May 30 2000

Keywords

Examples

			5 can be expressed as 5 or 2+3, so 5 is in the sequence.

References

  • R. K. Guy, Unsolved Problems in Number Theory, section C2.

Links

Crossrefs

Cf. A054845, A054859, A054996, A054998, A054999, A055500, A055001.

Formula

A054845(a(n)) = 2. - Ray Chandler, Sep 20 2023

A055001 Integers that can be expressed as the sum of consecutive primes in exactly 6 ways.

Original entry on oeis.org

34421, 130638, 229841, 235493, 271919, 295504, 345011, 347856, 358446, 358877, 414221, 429804, 434669, 480951, 488603, 532423, 532823, 543625, 561375, 621937, 626852, 655561, 687496, 703087, 734069, 746829, 810418, 824099, 888793
Offset: 1

Views

Author

Jud McCranie, May 30 2000

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, section C2.

Links

Crossrefs

Cf. A054845, A054859, A054996, A054997, A054998, A054999, A055000.

Formula

A054845(a(n)) = 6. - Ray Chandler, Sep 20 2023

A055000 Integers that can be expressed as the sum of consecutive primes in exactly 5 ways.

Original entry on oeis.org

311, 863, 14369, 14699, 15329, 16277, 19717, 20272, 25416, 28500, 29033, 36467, 37607, 40433, 41074, 42463, 45101, 46660, 48731, 49253, 49499, 50560, 53424, 55813, 59068, 67141, 68787, 70104, 70429, 70692, 71548, 76423, 78756, 78791
Offset: 1

Views

Author

Jud McCranie, May 30 2000

Keywords

References

  • R. K. Guy, Unsolved Problems in Number Theory, section C2.

Links

Crossrefs

Cf. A054845, A054859, A054996, A054997, A054998, A054999, A055001.

Formula

A054845(a(n)) = 5. - Ray Chandler, Sep 20 2023

A067373 Integers expressible as the sum of (at least two) consecutive primes in at least 3 ways.

Original entry on oeis.org

240, 287, 311, 340, 371, 510, 660, 803, 863, 864, 931, 961, 990, 1012, 1060, 1099, 1104, 1151, 1164, 1236, 1313, 1320, 1367, 1392, 1524, 1643, 1650, 1710, 1788, 1793, 1854, 1951, 1956, 2040, 2303, 2304, 2387, 2393, 2436, 2507, 2556, 2586, 2647, 2670
Offset: 1

Views

Author

Patrick De Geest, Feb 04 2002

Keywords

Examples

			240 = (113 + 127) = (53 + 59 + 61 + 67) = (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43) or (#2,113) (#4,53) (#8,17).

Links

Crossrefs

Cf. A050936, A067372-A067381, A054998.

Programs

  • Mathematica
    m=3*5!; lst={}; Do[p=Prime[a]; Do[p+=Prime[b]; If[pVladimir Joseph Stephan Orlovsky, Aug 15 2009 *)

Formula

A084143(a(n)) > 2. - Ray Chandler, Sep 20 2023

Extensions

Offset corrected by Donovan Johnson, Nov 14 2013

A291921 Numbers that are the sum of (at least two) consecutive primes in exactly three ways.

Original entry on oeis.org

240, 287, 340, 371, 510, 660, 803, 864, 931, 961, 990, 1012, 1060, 1099, 1104, 1151, 1236, 1313, 1367, 1392, 1524, 1643, 1710, 1788, 1793, 1951, 1956, 2040, 2303, 2304, 2387, 2393, 2436, 2507, 2556, 2586, 2647, 2670, 2689, 2706, 2886, 3010, 3166, 3232, 3263
Offset: 1

Views

Author

Arkadiusz Wesolowski, Sep 05 2017

Keywords

Examples

			240 is in the sequence because it can be written in exactly three ways as a sum of consecutive primes: 113 + 127, 53 + 59 + 61 + 67, and 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43.

Links

  • Eric Weisstein's World of Mathematics, Prime Sums

Crossrefs

Cf. A054998, A067373.

Programs

  • Magma
    lst1:=[]; lst3:=[]; r:=3263; s:=PrimesUpTo(Floor(r-r/3)); t:=#s; y:=0; w:=0; z:=1; while y le r do y+:=NthPrime(z); w+:=1; z+:=1; end while; for q in [1..NthPrime(w-1)] do for a in [1..t-q] do c:=&+[s[b]: b in [a..a+q]]; if c gt r then break; else Append(~lst1, c); end if; end for; end for; lst2:=Sort(lst1); x:=#lst2; for n in [1..r] do d:=Position(lst2, n); if d ge 1 and d+2 le x then e:=[lst2[f]: f in [d..d+2]]; if Min(e) eq Max(e) then if d+3 gt x then Append(~lst3, n); else if not lst2[d+3] eq n then Append(~lst3, n); end if; end if; end if; end if; end for; lst3;
Showing 1-7 of 7 results.

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

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