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.

A135548 Numbers in A134651 which are the sum of two terms from A001043 in a unique way.

Original entry on oeis.org

10, 13, 16, 17, 20, 23, 24, 26, 29, 30, 32, 35, 38, 41, 44, 47, 50, 57, 64, 65, 68, 70, 73, 80, 82, 83, 88, 89, 94, 95, 105, 110, 117, 118, 125, 133, 140, 143, 148, 149, 154, 157, 167, 176, 177, 178, 182, 191, 192, 200, 203, 208, 209, 215, 221, 227, 236, 242
Offset: 1

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Author

Zak Seidov, Feb 15 2008

Keywords

Comments

Numbers that are the sum of two terms of A001043, but not sum of a different pair of two terms.

Examples

			Recall that A001043 begins with 5,8,12,18,24,30,36,42,52,60,68,78,84,90, ...
So 48 is not in the sequence because 48 = 18+30 = 24+24.
But 88 is in the sequence as it is only = 52+36.
And 89 is there too because = 84+5.

Crossrefs

Cf. A001043, A134651, A135045.

Programs

  • PARI
    issum(i, vss) = {nb = 0; for (j = 1, #vss, if (vss[j] > i, break); for (k = 1, j, sv = vss[j] + vss[k]; if (sv == i, nb++); if (sv > i, break););); return (nb == 1);}
lista(nn) = {vec = vector(nn, i, i); vss = select(i->((precprime((i-1)/2) + nextprime(i/2) == i) && (i>2)), vec); for (i = 1, nn, if (issum(i, vss), print1(i, ", ")););} \\ Michel Marcus, Oct 14 2013

Extensions

Example, corrected and extended by Michel Marcus, Oct 14 2013

A134650 Numbers that are the sum of two consecutive primes (i.e., in A001043) but are not the sum of two sums of two consecutive primes.

Original entry on oeis.org

5, 8, 12, 18, 52, 100, 946
Offset: 1

Views

Author

N. J. A. Sloane, Jan 25 2008

Keywords

Comments

Numbers in A001043 but not in A134651.
Conjectured to be finite, may be complete.
a(8), if it exists, is greater than 20100000. - R. J. Mathar, Jan 26 2008

References

  • R. K. Guy, ed., Unsolved Problems, Western Number Theory Meeting, Las Vegas, 1988.

Crossrefs

Cf. A001043, A134651, A135045.

Programs

  • Maple
    with(numtheory): Sset := {}: for i to 15000 do Sset := `union`(Sset, {ithprime(i) + ithprime(i + 1)}) od: Sset := convert(Sset, list): for n from 1 to nops(Sset) do count := 0: s := Sset[n]: for i from 1 to n do if member(s - Sset[i], Sset) and s-Sset[i] >= s/2 then count := count + 1 fi; od: if count = 0 then printf(`%d,`, Sset[n]) fi; od: # James Sellers, Jan 28 2008

Extensions

946 found by James Sellers, Jan 25 2008

A135045 Numbers in A001043 which are the sum of two terms from A001043 in a unique way.

Original entry on oeis.org

24, 30, 68, 268, 434, 520
Offset: 1

Views

Author

Manuel Valdivia, Feb 10 2008; definition corrected Feb 15 2008

Keywords

Comments

A subsequence of A001043 INTERSECT A134651.

Examples

			24 = 12 + 12, A001043(5) = A001043(3) + A001043(3)
30 = 12 + 18, A001043(6) = A001043(3) + A001043(4)
68 = 8 + 60, A001043(11) = A001043(2) + A001043(10)
268 = 52 + 216, A001043(32) = A001043(9) + A001043(28)
434 = 24 + 410, A001043(47) = A001043(5) + A001043(46)
520 = 12 + 508, A001043(55) = A001043(3) + A001043(54)

Crossrefs

Cf. A134651, A001043, A134650, A135548.
Showing 1-3 of 3 results.

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

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