A298077 Oblong numbers that are the sum of 2 successive primes.

12, 30, 42, 90, 210, 240, 462, 600, 702, 930, 1482, 1560, 1722, 2352, 2862, 2970, 6162, 6480, 6642, 7656, 8010, 8556, 10920, 13572, 13806, 14280, 14762, 15006, 15750, 16002, 21462, 22350, 22650, 23562, 24492, 25122, 27060, 27390, 29070, 29412, 34410, 34782

Offset

1,1

Comments

Is this sequence infinite?

Includes all n*(n+1) for which n*(n+1)/2 - 2 and n*(n+1)/2 + 2 are prime. The generalized Bunyakovsky conjecture implies there are infinitely many of these. - Robert Israel, Feb 11 2018

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!

Example

a(4)=90 because 90 is oblong (i.e., 9*10) and the sum of 2 successive primes (i.e., 43+47).

Maple

filter:= proc(n) not isprime(n/2) and prevprime(n/2)+nextprime(n/2) = n end proc:
select(filter, [seq(n*(n+1), n=2..200)]); # Robert Israel, Feb 11 2018

Mathematica

Select[Total /@ Partition[Prime@ Range[2^11], 2, 1], IntegerQ@ Sqrt[4 # + 1] &] (* Michael De Vlieger, Jan 11 2018 *)

Prog

(PARI) isok(n) = my(p = 2); forprime(q=3, n, if (p+q==n, return (1)); p = q);
lista(nn) = {for (n=1, nn, m = n*(n+1); if (isok(m), print1(m, ", ")); ); } \\ Michel Marcus, Jan 13 2018
(Python)
from __future__ import division
from sympy import prevprime, nextprime, isprime
A298077_list = [n*(n+1) for n in range(3, 10**4) if prevprime(n*(n+1)//2) + nextprime(n*(n+1)//2) == n*(n+1)] # Chai Wah Wu, Feb 11 2018

Crossrefs

Intersection of A001043 and A002378.

Cf. A111163, A258044.

Sequence in context: A145470 A108278 A364975 * A135502 A256620 A125582

Adjacent sequences: A298074 A298075 A298076 * A298078 A298079 A298080

Keyword

nonn

Author

G. L. Honaker, Jr., Jan 11 2018

Status

approved