A121862 Least previously nonoccurring positive integer such that partial sum + 2 is prime.

1, 2, 6, 8, 4, 14, 10, 12, 20, 18, 16, 24, 26, 28, 32, 34, 36, 38, 22, 30, 48, 56, 54, 46, 44, 42, 60, 40, 50, 58, 66, 62, 52, 68, 64, 84, 90, 72, 92, 70, 96, 80, 94, 78, 104, 76, 74, 106, 102, 110, 88, 98, 82, 108, 114, 126, 116, 118, 86, 100, 120, 144, 122, 130, 128, 136

Offset: 1

Author

Jonathan Vos Post, Aug 30 2006

Keywords

• easy
• nonn

Comments

The sequence is the union of {1} and a permutation of even positive integers. The corresponding partial sums + 1 are 3, 5, 11, 19, 23, 37, 47, 59, 79, 97, 113, 137, 163, 191, 223. See A084758. - Zak Seidov, Feb 10 2015

Or, first differences of A084758. - Zak Seidov, Feb 10 2015

Examples

			a(1) = 1 because 1+2 = 3 is prime.
a(2) = 2 because 1+2+2 = 5 is prime.
a(3) = 6 because 1+2+6+2 = 11 is prime.
a(4) = 8 because 1+2+6+8+2 = 19 is prime.
a(5) = 4 because 1+2+6+8+4+2 = 23 is prime.
		

Links

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

Crossrefs

Cf. A000040, A121861.

Cf. A084758. - Zak Seidov, Feb 10 2015

Programs

Maple

M:= 300: # to get all entries before the first entry > N
a[1]:= 1:
s:= 3:
R:= {seq(2*i,i=1..M/2)}:
found:= true:
for n from 2 while found do
  found:= false;
  for r in R do
    if isprime(s+r) then
      a[n]:= r;
      s:= s + r;
      R:= R minus {r};
      found:= true;
      break
    fi
   od:
od:
seq(a[i],i=1..n-2); # Robert Israel, Feb 10 2015

Mathematica

f[s_] := Append[s, k = 1; p = 2 + Plus @@ s; While[MemberQ[s, k] || ! PrimeQ[p + k], k++ ]; k]; Nest[f, {}, 67] (* Robert G. Wilson v, Aug 31 2006 *)

Formula

a(n) = MIN{k>0 such that 2 + k + SUM[i=1..n-1]a(i) is prime and k <> a(i)}.

Extensions

More terms from Robert G. Wilson v, Aug 31 2006