A257974 Prime numbers that are not the sum of one or more consecutive triangular numbers.

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

Offset: 1

Author

Vicente Izquierdo Gomez, Nov 05 2015

Keywords

• nonn

Comments

Subsequence of primes of A050941. - Michel Marcus, Dec 14 2015

Prime numbers that are not the difference of two tetrahedral numbers (A000292). - Franklin T. Adams-Watters, Dec 16 2015

Examples

			From _Michael De Vlieger_, Nov 06 2015: (Start)
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)
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A050941, A000217, A000292, A125602, A269414.

Programs

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;
end do: # R. J. Mathar, Dec 14 2015

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 *)

Extensions

More terms from Michael De Vlieger, Nov 06 2015