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A298077
Oblong numbers that are the sum of 2 successive primes.
1
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
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.
Sequence in context: A145470 A108278 A364975 * A135502 A256620 A125582
KEYWORD
nonn
AUTHOR
G. L. Honaker, Jr., Jan 11 2018
STATUS
approved