A330502 - OEIS

%I #21 Dec 23 2024 14:53:46

%S 2,1,3,0,5,7,7,9,13,16,11,13,13,16,15,22,18,19,28,21,21,31,23,33,25,

%T 27,27,34,33,32,43,33,33,52,35,38,37,39,43,46,42,43,43,53,46,52,47,49,

%U 58,51,51,58,53,56,55,57,58,64,63,61,61,64,64,73,65,67,67,69,73,79,71,81

%N Least m >= n such that m(m+1)/2 - n(n-3)/2 is prime, or 0 if no such m exists.

%C a(n) - n + 1 is the number of steps to reach a prime in the game described by Peter Luschny on the SeqFan list (cf. link): Start with n, then add m = n, n+1, n+2,... until a prime is reached.

%C See A330501 for the resulting prime, A329946 for the primes never reached.

%H M. F. Hasler, <a href="/A330502/b330502.txt">Table of n, a(n) for n = 0..10000</a>

%H Peter Luschny, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2019-December/">Hopping for primes</a>, SeqFan list, Dec 13 2019.

%t Array[If[# == 3, 0, Block[{m = #}, While[! PrimeQ[m (m + 1)/2 - # (# - 3)/2], m++]; m]] &, 72, 0] (* _Michael De Vlieger_, Dec 16 2019 *)

%o (PARI) apply( {A330502(n,p=n)=if(n!=3,while(!isprime(p+=n),n++);n)}, [0..199])

%Y Cf. A000217 (triangular numbers n(n+1)/2), A000096 (n(n+3)/2), A330501 (the final prime reached), A329946 (primes never reached).

%K nonn

%O 0,1

%A _M. F. Hasler_, following an idea by _Peter Luschny_, Dec 16 2019