

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
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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..n1]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..n2); # 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



