A125718 a(1)=1. a(n) = the smallest positive integer not occurring earlier in the sequence such that the n-th prime is congruent to a(n) (mod n).

1, 3, 2, 7, 6, 13, 10, 11, 5, 9, 20, 25, 15, 29, 17, 21, 8, 43, 48, 31, 52, 35, 14, 41, 22, 23, 49, 51, 80, 53, 34, 67, 38, 37, 44, 79, 46, 87, 50, 93, 56, 55, 19, 61, 62, 107, 70, 127, 129, 179, 131, 83, 82, 89, 92, 39, 98, 97, 100, 101, 161, 45, 118, 119, 183, 185, 63, 65

Offset: 1

Author

Leroy Quet, Feb 01 2007

Keywords

• nonn

Comments

This sequence seems likely to be a permutation of the positive integers. It will be if every positive number appears in A004648 (cf. A127149, A127150).

If this is a permutation of the positive integers, then A249678 is the inverse permutation. - M. F. Hasler, Nov 03 2014

Links

• Ferenc Adorjan, Table of n,a(n) for n=1,10000
• Ferenc Adorjan, Some characteristics of _Leroy Quet_'s permutation sequences
• Ferenc Adorjan, More about the structure of _Leroy Quet_'s sequences A125715, A125717, A125718 & A125727

Crossrefs

Cf. A004648.

Programs

Mathematica

f[l_List] := Block[{n = Length[l] + 1, k = Mod[Prime[n], n, 1]},While[MemberQ[l, k], k += n];Append[l, k]];Nest[f, {1}, 70] (* Ray Chandler, Feb 04 2007 *)

PARI

{Quet_p3(n)= /* Permutation sequence a'la Leroy Quet, A125718 */local(x=[1],k=0,w=1); for(i=2,n,if((k=prime(i)%i)==0,k=i);while(bittest(w,k-1)>0,k+=i);x=concat(x,k);w+=2^(k-1));return(x)}

PARI

A125718(n,show=0,u=1)={for(n=1,n,p=prime(n)%n;while(bittest(u,p),p+=n);u+=1<M. F. Hasler, Nov 03 2014

Extensions

Extended by Ray Chandler, Feb 04 2007