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.

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A212888 Conjectured number of positive even numbers that can be represented as the sum of two twin primes p + q in exactly n ways, with p >= q.

Original entry on oeis.org

35, 115, 285, 327, 557, 537, 723, 652, 882, 773, 1061, 916, 1158, 1069, 1369, 1143, 1436, 1307, 1566, 1318, 1711, 1336, 1752, 1380, 1798, 1480, 1847, 1449, 2012, 1556, 1967, 1599, 2184, 1646, 2257, 1656, 2278, 1779, 2376, 1786, 2353, 1823, 2523, 1832, 2415
Offset: 0

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Author

Michael Jones, May 29 2012

Keywords

Comments

For even n, a(n) - a(n-1) increases as n increases.

Crossrefs

Cf. A001097 (twin primes).
Cf. A007534 (35 numbers that have no representation).
Cf. A129363 (number of partitions of 2n into the sum of two twin primes).
Cf. A212613 (last number having n representations).

Programs

  • Mathematica
    p = Prime[Range[10000]]; tp = Select[p, PrimeQ[# + 2] || PrimeQ[# - 2] &]; {tn, t} = Transpose[Sort[Tally[Select[Flatten[Table[If[a >= b, a + b, 0], {a, tp}, {b, tp}]], # < tp[[-1]] &]]]]; Join[{Length[Complement[Range[2, tn[[-1]], 2], tn]]}, Table[Count[t, n], {n, 8}]] (* T. D. Noe, May 30 2012 *)

Extensions

Extended and corrected by T. D. Noe, May 30 2012

A352305 a(n) is the (conjectured) largest even number that can be expressed as the sum of two distinct primes in exactly n ways.

Original entry on oeis.org

6, 38, 68, 128, 158, 188, 398, 362, 458, 542, 632, 692, 602, 992, 808, 908, 1112, 1238, 1412, 1418, 1718, 1544, 1574, 1622, 1682, 2048, 2252, 2018, 2672, 2042, 2558, 2936, 2504, 2978, 2966, 3092, 3218, 3242, 3272, 3506, 3632, 3754, 4022, 4058, 4052, 4412, 4448, 4478
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 11 2022

Keywords

Examples

			a(5) = 188 because 188 = 7 + 181 = 31 + 157 = 37 + 151 = 61 + 127 = 79 + 109 and it is conjectured that 188 is the last term of A080854.
		

Crossrefs

Extensions

More terms from Hugo Pfoertner, Dec 18 2024
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