

A125718


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


3



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
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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] (*Chandler*)


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, k1)>0, k+=i); x=concat(x, k); w+=2^(k1)); 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: A122355 A175433 A058646 * 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



