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

Author

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

Keywords

• nonn

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

Examples

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

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios!

Crossrefs

Intersection of A001043 and A002378.

Cf. A111163, A258044.

Programs

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 *)

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