cp's OEIS Frontend

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

%I A298077 #27 Apr 03 2023 10:36:13
%S A298077 12,30,42,90,210,240,462,600,702,930,1482,1560,1722,2352,2862,2970,
%T A298077 6162,6480,6642,7656,8010,8556,10920,13572,13806,14280,14762,15006,
%U A298077 15750,16002,21462,22350,22650,23562,24492,25122,27060,27390,29070,29412,34410,34782
%N A298077 Oblong numbers that are the sum of 2 successive primes.
%C A298077 Is this sequence infinite?
%C A298077 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
%H A298077 Chai Wah Wu, <a href="/A298077/b298077.txt">Table of n, a(n) for n = 1..10000</a>
%H A298077 G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/page.php?curio_id=31795">Prime Curios!</a>
%e A298077 a(4)=90 because 90 is oblong (i.e., 9*10) and the sum of 2 successive primes (i.e., 43+47).
%p A298077 filter:= proc(n) not isprime(n/2) and prevprime(n/2)+nextprime(n/2) = n end proc:
%p A298077 select(filter, [seq(n*(n+1), n=2..200)]); # _Robert Israel_, Feb 11 2018
%t A298077 Select[Total /@ Partition[Prime@ Range[2^11], 2, 1], IntegerQ@ Sqrt[4 # + 1] &] (* _Michael De Vlieger_, Jan 11 2018 *)
%o A298077 (PARI) isok(n) = my(p = 2); forprime(q=3, n, if (p+q==n, return (1)); p = q);
%o A298077 lista(nn) = {for (n=1, nn, m = n*(n+1); if (isok(m), print1(m, ", ")););} \\ _Michel Marcus_, Jan 13 2018
%o A298077 (Python)
%o A298077 from __future__ import division
%o A298077 from sympy import prevprime,nextprime,isprime
%o A298077 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
%Y A298077 Intersection of A001043 and A002378.
%Y A298077 Cf. A111163, A258044.
%K A298077 nonn
%O A298077 1,1
%A A298077 _G. L. Honaker, Jr._, Jan 11 2018