A277618 Lexicographically earliest nonnegative sequence such that |a(n+1)-a(n)| is a prime number, and no number occurs twice; a(0) = 0.

0, 2, 4, 1, 3, 5, 7, 9, 6, 8, 10, 12, 14, 11, 13, 15, 17, 19, 16, 18, 20, 22, 24, 21, 23, 25, 27, 29, 26, 28, 30, 32, 34, 31, 33, 35, 37, 39, 36, 38, 40, 42, 44, 41, 43, 45, 47, 49, 46, 48, 50, 52, 54, 51, 53, 55, 57, 59, 56, 58, 60, 62, 64, 61, 63, 65, 67, 69, 66, 68, 70, 72, 74, 71, 73, 75, 77, 79, 76, 78, 80, 82, 84, 81, 83, 85, 87, 89, 86, 88, 90

Offset: 0

Author

Eric Angelini and M. F. Hasler, Oct 23 2016

Keywords

• nonn
• easy

Comments

A variant of A277616, which is defined in a similar way with squares > 1 instead of primes.

The steps a(n+1)-a(n) are either +2 or -3, after 10 terms we get a(n+10), and the first 10 terms are all numbers between 0 and 9: This sequence is obviously a permutation of the nonnegative integers, with a(n) = a(n-5) + 5 for all n > 5. The strictly positive variant (starting with a(1) = 1) is given by A065186.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Crossrefs

Cf. A277616, A277617, A065186.

Programs

Mathematica

Table[n - 2 + Mod[n - 3, 5], {n, 0, 500}] (* Fred Patrick Doty, Aug 03 2020 *)

PARI

{u=[a=0];(chk(n)=(!#u||(n>u[1]&&!setsearch(u,n)))&&(u=setunion(u,[n]))&&!while(#u>1&&u[2]==u[1]+1,u=u[^1]));for(n=1,99,print1(a","); for(k=-primepi(a+!a-1),9e9, k||next; chk(a+sign(k)*prime(abs(k)))||next; a+=sign(k)*prime(abs(k));break))}

PARI

A277618(n,i=[0,2,4,1,3])=i[n%#i+1]+n\#i*#i

Formula

a(n) = a(n-5) + 5 for all n > 5.

a(n) = A065186(n+1) - 1.

G.f.: x*(2*x^4 + 2*x^3 - 3*x^2 + 2*x + 2)/(x^6 - x^5 - x + 1). - Chai Wah Wu, Mar 30 2023

Extensions

Offset corrected by R. J. Mathar, Jun 19 2021