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 1-5 of 5 results.

A332989 a(n) is the smallest number writable in n different ways as the sum of two distinct nonzero pentagonal numbers.

Original entry on oeis.org

6, 211, 2999, 13352, 205427, 250927, 1134927, 2177527, 5002427, 6422352, 17349697, 30135652, 45997927, 55075502, 168570052, 130917177, 101275552, 249483677, 441561407, 433742427, 771789552, 1546505052, 1316582177, 1701923302, 2288827477, 1073520852, 3110207127
Offset: 1

Views

Author

Olivier Gérard, Mar 05 2020

Keywords

Comments

I conjecture this sequence is infinite.

Examples

			211 can be written 35 + 176 and 1 + 210;
2999 can be written 852 + 2147, 247 + 2752, 117 + 2882;
13352 = P(52) + P(79) = P(29) + P(90) = P(17) + (93) = P(10) + P(94).

Links

Crossrefs

Cf. A000326, A332988.
Cf. A093195 (analog sequence for perfect squares).

Programs

  • PARI
    a(n) = for(k=1, oo, if(sum(i=1, sqrt(1+12*k)\6, sqrt(1+24*k+12*i-36*i*i)%6==5)==n, return(k))); \\ Jinyuan Wang, Mar 06 2020

Extensions

Name clarified by Jinyuan Wang, Mar 06 2020
Terms a(12) and beyond from Giovanni Resta, Mar 08 2020

A333011 Integers which can be written in only one way as a sum of two distinct nonzero pentagonal numbers.

Original entry on oeis.org

6, 13, 17, 23, 27, 34, 36, 40, 47, 52, 56, 57, 63, 71, 73, 75, 82, 86, 92, 93, 97, 104, 105, 114, 118, 121, 122, 127, 129, 139, 143, 146, 150, 152, 157, 162, 167, 168, 177, 180, 181, 187, 188, 196, 198, 209, 222, 227, 232, 237, 245, 246, 248, 252, 259, 261, 262
Offset: 1

Views

Author

Olivier Gérard, Mar 05 2020

Keywords

Comments

The first term of A332988 not in this sequence is 211.

Links

Crossrefs

Cf. A000326, A332988, A333011, A333012, A333013, A333014, A333015.

Programs

  • PARI
    is(k) = sum(i=1, sqrt(1+12*k)\6, sqrt(1+24*k+12*i-36*i*i)%6==5) == 1; \\ Jinyuan Wang, Mar 06 2020

A333014 Numbers which can written in exactly four ways as a sum of two distinct nonzero pentagonal numbers.

Original entry on oeis.org

13352, 18877, 45397, 49052, 52027, 53727, 62652, 64182, 73152, 74977, 76677, 79327, 80671, 85177, 87972, 88577, 90702, 91652, 93302, 96669, 98827, 101752, 106036, 106822, 109227, 109487, 116117, 118477, 125347, 133267, 135786, 138087, 138802, 140852, 141532, 144747, 145302, 145641, 147274, 148077, 148927
Offset: 1

Views

Author

Olivier Gérard, Mar 05 2020

Keywords

Examples

			13352 = P(52) + P(79) = P(29) + P(90) = P(17) + P(93) = P(10) + P(94), where P(n) is the n-th pentagonal number A000326.

Crossrefs

Cf. A000326, A332988, A332989, A333011, A333012, A333013.

Programs

  • PARI
    is(k) = sum(i=1, sqrt(1+12*k)\6, sqrt(1+24*k+12*i-36*i*i)%6==5) == 4; \\ Jinyuan Wang, Mar 06 2020

A333007 Perfect squares that are sum of two nonzero pentagonal numbers.

Original entry on oeis.org

36, 121, 196, 400, 625, 1225, 1521, 3481, 5776, 7056, 7225, 8464, 8836, 9025, 9216, 10816, 11025, 11664, 13456, 15129, 15625, 16641, 17689, 18496, 21609, 23409, 24649, 25600, 28561, 30276, 32761, 34596, 35721, 36100, 36864, 37636, 38025, 39204, 40000, 42436, 42849
Offset: 1

Views

Author

Olivier Gérard, Mar 05 2020

Keywords

Examples

			36  = 6^2  = 1  + 35;
121 = 11^2 = 51 + 70;
196 = 14^2 = 51 + 145.

Links

Crossrefs

Cf. A000326, A332987, A332988, A333008, A333009.

Programs

  • PARI
    is(k) = issquare(k) && sum(i=1, sqrt(1+12*k)\6, sqrt(1+24*k+12*i-36*i*i)%6==5)>0; \\ Jinyuan Wang, Mar 06 2020

Extensions

More terms from Jinyuan Wang, Mar 06 2020

A333015 Numbers which can be written in exactly five ways as a sum of two distinct nonzero pentagonal numbers.

Original entry on oeis.org

205427, 210552, 230102, 269712, 333802, 346977, 354537, 384802, 397892, 416677, 420077, 426622, 448552, 470902, 471927, 478302, 509752, 520852, 563772, 566177, 569507, 571377, 575202, 580302, 586102, 590162, 599847, 610052, 616552, 618263, 635552, 646177, 647947
Offset: 1

Views

Author

Olivier Gérard, Mar 05 2020

Keywords

Examples

			205427 = P(234) + P(287) = P(201) + P(311) = P(166) + P(331) = P(56) + P(366) = P(49) + P(367), where P(n) is the n-th pentagonal number (A000326).

Crossrefs

Cf. A000326, A332988, A332989, A333011, A333012, A333013, A333014.

Programs

  • PARI
    is(k) = sum(i=1, sqrt(1+12*k)\6, sqrt(1+24*k+12*i-36*i*i)%6==5) == 5; \\ Jinyuan Wang, Mar 06 2020

Extensions

More terms from Jinyuan Wang, Mar 06 2020
Showing 1-5 of 5 results.

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