OFFSET
1,2
COMMENTS
These numbers are the t in sequence A152900, sorted and duplicates removed. It is not possible for all four numbers to be prime because when t is odd either (t-1)/2 or (t+1)/2 must be even.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
10 is here because 19 is prime. 15 is here because 7, 29 and 31 are prime.
MAPLE
f:= proc(n) local t; t:= n*(n+1)/2; if ormap(x -> x::integer and isprime(x), [(t-1)/2, (t+1)/2, 2*t-1, 2*t+1]) then t else NULL fi end proc:
map(f, [$1..100]); # Robert Israel, Dec 28 2023
MATHEMATICA
nn=100; Select[Range[nn]*Range[2, 1+nn]/2, PrimeQ[(#-1)/2] || PrimeQ[(#+1)/2] || PrimeQ[2#-1] || PrimeQ[2#+1] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Dec 14 2008
STATUS
approved