The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A125718 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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).
(history; published version)

#21 by Ray Chandler at Thu Oct 10 15:34:06 EDT 2019

STATUS

editing

approved

#20 by Ray Chandler at Thu Oct 10 15:34:03 EDT 2019

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 *)

STATUS

approved

editing

#19 by Bruno Berselli at Tue Nov 04 03:19:08 EST 2014

STATUS

reviewed

approved

#18 by Joerg Arndt at Tue Nov 04 03:06:33 EST 2014

STATUS

proposed

reviewed

#17 by M. F. Hasler at Mon Nov 03 21:49:57 EST 2014

STATUS

editing

proposed

#16 by M. F. Hasler at Mon Nov 03 21:49:36 EST 2014

COMMENTS

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

PROG

(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

STATUS

approved

editing

#15 by Charles R Greathouse IV at Wed Apr 09 10:13:02 EDT 2014

AUTHOR

Leroy Quet , Feb 01 2007

Discussion

Wed Apr 09

10:13

OEIS Server: https://oeis.org/edit/global/2146

#14 by Charles R Greathouse IV at Tue Mar 11 01:32:20 EDT 2014

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)}

Discussion

Tue Mar 11

01:32

OEIS Server: https://oeis.org/edit/global/2122

#13 by N. J. A. Sloane at Wed Feb 05 20:18:29 EST 2014

LINKS

Ferenc Adorjan, <a href="http://web.t-online.hu/fadorjan/l_quet.pdf">Some characteristics of _Leroy Quet_'s permutation sequences</a>

Ferenc Adorjan, <a href="http://web.axelero.hu/fadorjan/l_quet.pdf">More about the structure of _Leroy Quet_'s sequences A125715, A125717, A125718 & A125727</a>

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)}

AUTHOR

_Leroy Quet _ Feb 01 2007

Discussion

Wed Feb 05

20:18

OEIS Server: https://oeis.org/edit/global/2118

#12 by N. J. A. Sloane at Wed Feb 05 20:11:57 EST 2014

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)}

Discussion

Wed Feb 05

20:11

OEIS Server: https://oeis.org/edit/global/2117