A135045 -id:A135045 - cp's OEIS frontend

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.

5, 8, 12, 18, 52, 100, 946

Offset: 1

N. J. A. Sloane, Jan 25 2008

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

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

Cf. A001043, A134651, A135045.

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

946 found by James Sellers, Jan 25 2008

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

Zak Seidov, Feb 15 2008

nonn

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

			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.

Cf. A001043, A134651, A135045.

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

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

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

References

Crossrefs

Programs

Maple

Extensions