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A152899
Triangular numbers t such that (t-1)/2, (t+1)/2, 2t-1 or 2t+1 is prime.
2
1, 3, 6, 10, 15, 21, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 190, 210, 231, 253, 300, 325, 351, 378, 406, 465, 496, 561, 630, 741, 780, 861, 990, 1035, 1081, 1176, 1225, 1275, 1431, 1485, 1540, 1596, 1653, 1770, 1830, 1953, 2080, 2145, 2211, 2346, 2415
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
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
Sequence in context: A365699 A346735 A174163 * A352212 A342212 A061304
KEYWORD
nonn
AUTHOR
T. D. Noe, Dec 14 2008
STATUS
approved