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