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

1,1

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

Links

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

Example

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)

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 *)

Crossrefs

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

Sequence in context: A245063 A168033 A331486 * A323782 A020591 A197188

Adjacent sequences: A257971 A257972 A257973 * A257975 A257976 A257977

Keyword

nonn

Author

Vicente Izquierdo Gomez, Nov 05 2015

Extensions

More terms from Michael De Vlieger, Nov 06 2015

Status

approved