OFFSET
1,2
COMMENTS
The sequence is well-defined (the terms must alternate in parity, and by Dirichlet's theorem a(n+1) always exists). - N. J. A. Sloane, Mar 07 2017
Does every positive integer eventually occur? - Dmitry Kamenetsky, May 27 2009. Reply from Robert G. Wilson v, May 27 2009: The answer is almost certainly yes, on probabilistic grounds.
It appears that this is the limit of the rows of A051237. That those rows do approach a limit seems certain, and given that that limit exists, that this sequence is the limit seems even more likely, but no proof is known for either conjecture. - Robert G. Wilson v, Mar 11 2011, edited by Franklin T. Adams-Watters, Mar 17 2011
LINKS
Zak Seidov, Table of n, a(n) for n = 1..10000 (First 1000 terms from T. D. Noe)
N. J. A. Sloane, Table of n, a(n) for n = 1..100000 (computed using Orlovsky's Mma program)
M. F. Hasler, Prime sums from neighboring terms, OEIS Wiki, Nov. 23, 2019
FORMULA
EXAMPLE
a(5) = 7 because 1, 2, 3 and 4 have already been used and neither 4 + 5 = 9 nor 4 + 6 = 10 are prime while 4 + 7 = 11 is prime.
MAPLE
A055265 := proc(n)
local a, i, known ;
option remember;
if n =1 then
1;
else
for a from 1 do
known := false;
for i from 1 to n-1 do
if procname(i) = a then
known := true;
break;
end if;
end do:
if not known and isprime(procname(n-1)+a) then
return a;
end if;
end do:
end if;
end proc:
seq(A055265(n), n=1..100) ; # R. J. Mathar, Feb 25 2017
MATHEMATICA
f[s_List] := Block[{k = 1, a = s[[ -1]]}, While[ MemberQ[s, k] || ! PrimeQ[a + k], k++ ]; Append[s, k]]; Nest[f, {1}, 71] (* Robert G. Wilson v, May 27 2009 *)
q=2000; a={1}; z=Range[2, 2*q]; While[Length[z]>q-1, k=1; While[!PrimeQ[z[[k]]+Last[a]], k++]; AppendTo[a, z[[k]]]; z=Delete[z, k]]; Print[a] (*200 times faster*) (* Vladimir Joseph Stephan Orlovsky, May 03 2011 *)
PROG
(HP 50G Calculator) << DUPDUP + 2 -> N M L << { 1 } 1 N 1 - FOR i L M FOR j DUP j POS NOT IF THEN j DUP 'L' STO M 'j' STO END NEXT OVER i GET SWAP WHILE DUP2 + DUP ISPRIME? NOT REPEAT DROP DO 1 + 3 PICK OVER POS NOT UNTIL END END ROT DROP2 + NEXT >> >> Gerald Hillier, Oct 28 2008
(Haskell)
import Data.List (delete)
a055265 n = a055265_list !! (n-1)
a055265_list = 1 : f 1 [2..] where
f x vs = g vs where
g (w:ws) = if a010051 (x + w) == 1
then w : f w (delete w vs) else g ws
-- Reinhard Zumkeller, Feb 14 2013
(PARI) v=[1]; n=1; while(n<50, if(isprime(v[#v]+n)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0); n++); v \\ Derek Orr, Jun 01 2015
(PARI) U=-a=1; vector(100, k, k=valuation(1+U+=1<<a, 2); while(bittest(U, k)|| !isprime(a+k), k++); a=k) \\ M. F. Hasler, Feb 11 2020
CROSSREFS
Inverse permutation: A117922; fixed points: A117925; A117923=a(a(n)). - Reinhard Zumkeller, Apr 03 2006
Cf. A086527 (the primes a(n)+a(n-1)).
Cf. A070942 (n's such that a(1..n) is a permutation of (1..n)). - Zak Seidov, Oct 19 2011
See A282695 for deviation from identity sequence.
A073659 is a version where the partial sums must be primes.
KEYWORD
easy,nice,nonn
AUTHOR
Henry Bottomley, May 09 2000
EXTENSIONS
Corrected by Hans Havermann, Sep 24 2002
STATUS
approved