A255004 Lexicographically earliest permutation of positive integers such that a(a(n)+a(n+1)) is prime for all n.

1, 2, 3, 4, 5, 6, 7, 8, 11, 9, 13, 10, 17, 12, 19, 14, 15, 16, 23, 29, 18, 31, 37, 20, 21, 22, 41, 24, 43, 25, 47, 26, 53, 27, 28, 30, 32, 33, 59, 34, 61, 35, 67, 36, 38, 39, 71, 40, 73, 42, 44, 79, 45, 46, 83, 48, 89, 97, 49, 50, 51, 101, 103, 52, 107, 54

Offset: 1

Author

Eric Angelini and M. F. Hasler, Feb 11 2015

Keywords

• nonn

Comments

This is the sequence V defined in the Comments on A255003.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A255003, A256210.

For indices of primes see A256212.

Programs

Maple

N:= 100: # to get a(n) for n <= N
maxprime:= 2:
maxa:= 2:
a[1]:= 1:
a[2]:= 2:
needprime:= {3}:
for n from 3 to N do
  if member(n,needprime) then
     a[n]:= nextprime(maxprime);
     maxprime:= a[n];
  else
     if isprime(maxa+1) and maxa+1<= maxprime then a[n]:= maxa+2
     else a[n]:= maxa+1
     fi;
     maxa:= a[n];
  fi;
  needprime:= needprime union {a[n-1]+a[n]};
od:
seq(a[n],n=1..N); # Robert Israel, Mar 26 2015

Mathematica

M = 100;
maxprime = 2; maxa = 2; a[1] = 1; a[2] = 2; needprime = {3}; For[n = 3, n <= M, n++, If[MemberQ[needprime, n], a[n] = NextPrime[maxprime]; maxprime = a[n], If[PrimeQ[maxa+1] && maxa+1 <= maxprime, a[n] = maxa+2, a[n] = maxa+1]; maxa = a[n]]; needprime = needprime ~Union~ {a[n-1] + a[n]}];
Array[a, M] (* Jean-François Alcover, Mar 22 2019, after Robert Israel *)

PARI

{a=vector(100,i,1); u=[1]/* used numbers beyond u[1] */; for(n=2,#a, if( a[n] < 0, a[n]=u[1]; while(setsearch(u,a[n]++)||!isprime(a[n]),), a[n]=u[1]; while(setsearch(u,a[n]++),)); u=setunion(u,[a[n]]); while( #u>1 && u[2]==u[1]+1, u=u[2..#u]); a[n]+a[n-1]>#a || a[a[n]+a[n-1]]=-1)}