A051884 Smallest number larger than the previous term which is not a prime but is relatively prime to the previous term.

1, 4, 9, 10, 21, 22, 25, 26, 27, 28, 33, 34, 35, 36, 49, 50, 51, 52, 55, 56, 57, 58, 63, 64, 65, 66, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 143, 144, 145, 146, 147, 148, 153, 154, 155, 156, 161, 162, 169

Offset: 1

Author

Felice Russo, Dec 15 1999

Keywords

• nonn
• nice
• easy

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• A. Murthy, Exploring some new ideas on Smarandache type sets, functions and sequences, Smarandache Notions Journal Vol. 11 N. 1-2-3 Spring 2000.

Crossrefs

Sequences with related definitions: A072525, A085084, A126638, A131368, A163643.

Cf. A002808.

Programs

Haskell

a051884 n = a051884_list !! (n-1)
a051884_list =  1 : f 1 a002808_list where
   f x cs = y : f y (dropWhile (<= y) cs) where
     y = head [z | z <- cs, x `gcd` z == 1]
-- Reinhard Zumkeller, Jun 03 2013

Maple

with(numtheory); i:=4; k:=5; while(k < 100) do while(order(k, i) = FAIL or isprime(k)) do k:=k+1; end do; print(k); i:= k; k:=k+1; end do; # Ben Paul Thurston, Feb 08 2007

Mathematica

rPrimeNext[n_]:=Module[{k},k=n+1;While[PrimeQ[k]||GCD[n,k]!=1,k++ ];k]; a=1;lst={a};Do[AppendTo[lst,a=rPrimeNext[a]],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, May 15 2010 *)
nxt[n_]:=Module[{k=n+1},While[PrimeQ[k]||!CoprimeQ[k,n],k++];k]; NestList[ nxt,1,60] (* Harvey P. Dale, Mar 12 2013 *)

Extensions

More terms from James Sellers, Dec 16 1999

Definition corrected by Franklin T. Adams-Watters, Sep 19 2006