A088047 Smallest prime(k) such that prime(k) - prime(j) == 0 (mod prime(n)), for some j < k.

5, 5, 7, 17, 13, 29, 19, 41, 53, 31, 67, 79, 43, 89, 97, 109, 61, 127, 137, 73, 149, 163, 173, 181, 197, 103, 211, 109, 223, 229, 257, 269, 139, 281, 151, 307, 317, 331, 337, 349, 181, 367, 193, 389, 199, 401, 433, 449, 229, 461, 479, 241, 487, 509, 521, 557

Offset

1,1

Comments

If prime(m), prime(m+1) form a twin prime pair then a(m) = prime(m+1).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(5) = 13 as 13-2 =11, a(8) = 41 as 41-3 = 38 = 2*19.

Maple

N:= 10000: # for terms before the first term > N
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
nP:= nops(P):
f:= proc(n)
   local p, S, j, m;
   S:= {}:
   p:= P[n];
   for j from 1 to nP do
     m:= P[j] mod p;
     if member(m, S) then return P[j] fi;
     S:= S union {m};
   od;
  FAIL
end proc:
R:= NULL:
for k from 1 do
 v:= f(k);
 if v = FAIL then break fi;
 R:= R, v
od:
R; # Robert Israel, Nov 04 2025

Prog

(PARI) r=Set(); forprime(n=2, 10^5, s=r; forprime(k=n, 10^5, if(setsearch(s, k%n), print1(" ", k); break, s=setunion(s, [k%n]))); r=setunion(r, [n])) \\ Max Alekseyev, Feb 14 2005

Crossrefs

Cf. A088046.

Sequence in context: A093307 A264388 A141392 * A109257 A088048 A006146

Adjacent sequences: A088044 A088045 A088046 * A088048 A088049 A088050

Keyword

nonn

Author

Amarnath Murthy, Sep 20 2003

Extensions

More terms from Max Alekseyev, Feb 14 2005

Status

approved