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A121862 Least previously nonoccurring positive integer such that partial sum + 2 is prime. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

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

FORMULA

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A000040, A121861.

Cf. A084758. - Zak Seidov, Feb 10 2015

Sequence in context: A115317 A117932 A073411 * A095677 A011045 A002210

Adjacent sequences:  A121859 A121860 A121861 * A121863 A121864 A121865

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Aug 30 2006

EXTENSIONS

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

STATUS

approved

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Last modified November 14 16:49 EST 2019. Contains 329126 sequences. (Running on oeis4.)