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

1,2

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

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 *)

Prog

(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<<p; show&&print1(p", ")/*a=concat(a, p)*/); p} \\ M. F. Hasler, Nov 03 2014

Crossrefs

Cf. A004648.

Sequence in context: A175433 A058646 A323635 * A268821 A014841 A056476

Adjacent sequences: A125715 A125716 A125717 * A125719 A125720 A125721

Keyword

nonn

Author

Leroy Quet, Feb 01 2007

Extensions

Extended by Ray Chandler, Feb 04 2007

Status

approved