A259019 Lexicographically first permutation of the nonnegative integers such that Sum_{k=n..2n} a(k) is a prime number, with a(1)=0.

0, 2, 1, 4, 3, 5, 6, 11, 7, 9, 8, 13, 10, 15, 12, 16, 14, 23, 17, 20, 18, 25, 19, 21, 22, 31, 24, 30, 26, 29, 27, 35, 28, 34, 32, 38, 33, 48, 36, 37, 39, 41, 40, 44, 42, 53, 43, 50, 45, 46, 47, 55, 49, 52, 51, 57, 54, 66, 56, 60, 58, 63, 59, 62, 61, 78, 64, 84

Offset: 1

Author

Michel Lagneau, Jun 16 2015

Keywords

• nonn

Comments

Previous name: a(1)=0; for n>1, a(n) is the least number not yet used having the property that a(n) added with the next n terms is a prime number.

The corresponding primes are 2, 7, 13, 29, 41, 59, 79, 101, 127, 157, 191, 223, 263, 307, 347, 397, 443, 499, 557, 613, 673, 739, 809, 883, 953, 1033, 1103, 1187, 1277, 1367, 1459, 1553, 1657, 1777, ...

This is a permutation of the integers. - Michel Marcus, Jun 21 2015

Examples

			a(1)= 0 plus the next single term 2 is 2 (a prime);
a(2)= 2 plus the next two terms (1,4) is 7 (a prime);
a(3)= 1 plus the next three terms (4,3,5) is 13 (a prime);
a(4)= 4 plus the next four terms (3,5,6,11) is 29 (a prime);
a(5)= 3 plus the next five terms (5,6,11,7,9) is 41 (a prime).
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000040, A247665, A259018.

Programs

Maple

nn:=100:T:=array(1..nn):T[1]:=0:T[2]:=2:kk:=2:lst:={0,2}:
for n from 2 to nn do:
  ii:=0:
    for k from 1 to 1000 while(ii=0)do:
     if {k} intersect lst = {}
     then
     ii:=1:lst:=lst union {k}:kk:=kk+1:T[kk]:=k:
     else
     fi:
    od:
     jj:=0:n0:=nops(lst):s:=sum('T[i]', 'i'=n..n0):
      for p from 1 to 100 while(jj=0) do:
        z:=s+p:
         if type(z,prime)=true and {p} intersect lst={}
         then
         jj:=1:lst:=lst union {p}:kk:=kk+1:T[kk]:=p:
         else
         fi:
       od:
od:
print(T):

Extensions

Name edited by Jon E. Schoenfield, Sep 12 2017