

A257974


Prime numbers that are not the sum of one or more consecutive triangular numbers.


2



2, 5, 7, 11, 13, 17, 23, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 89, 97, 101, 103, 107, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 211, 223, 227, 229, 233, 239, 241, 257, 263, 269, 271, 277, 281, 283
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OFFSET

1,1


COMMENTS



LINKS



EXAMPLE

3 is a triangular number thus is not a term.
The triangular numbers <= 7 are {1, 3, 6}. None of these are 7. 7 is not found among the sums of adjacent pairs of terms, i.e., {{1, 3}, {3, 6}} = {4, 9}. The sum of all numbers {1, 3, 6} = 10. Thus 7 is a term.
The triangular numbers <= 19 are {1, 3, 6, 10, 15}. 19 is not a triangular number. 19 is not found among sums of pairs of adjacent terms {4, 9, 16, 25} nor among those of quartets of adjacent terms {20, 34}, but is found among sums of triples of adjacent terms {10, 19, 31}. Thus 19 is not a term. (End)


MAPLE

isA257974 := proc(n)
if isprime(n) then
return not isA034706(n) ;
else
false ;
end if;
end proc:
for n from 0 to 400 do
if isA257974(n) then
printf("%d, ", n) ;
end if;


MATHEMATICA

t = Array[Binomial[# + 1, 2] &, {10^4}]; fQ[n_] := Block[{s}, s = TakeWhile[t, # <= n &]; AnyTrue[Flatten[Total /@ Partition[s, #, 1] & /@ Range[Length@ s  1]], # == n &]]; Select[Prime@ Range@ 120, ! fQ@ # &] (* Michael De Vlieger, Nov 06 2015, Version 10 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



