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A341640 a(n) is the first prime p such that each of the first n primes divides at least one of the composites between p and the next prime, but prime(n+1) does not divide any of these. 1
2, 3, 5, 7, 13, 19, 61, 211, 151, 181, 199, 113, 1069, 1129, 773, 3137, 887, 13187, 14087, 5351, 29881, 2477, 30727, 69263, 40289, 35677, 118973, 110359, 31397, 186481, 294563, 155921, 404851, 221327, 332317, 265621, 1665343, 544279, 1349533, 2124679, 1242643, 3826019, 7230331, 1444309, 5831401 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) >= A341650(n), with equality if and only if A341650(n) < A341650(n+1).

LINKS

Robert Israel, Table of n, a(n) for n = 0..78

EXAMPLE

a(7) = 211 because each of the first 7 primes divides at least one of the composites 212 to 222 (2|212, 3|213, 5|215, 7|217, 11|220, 13|221, 17|221), but the 8th prime 19 does not.

MAPLE

N:= 50: # for a(0) to a(N)

count:= 1:

P:= [seq(ithprime(i), i=1..N)]:

V:= Array(0..N): V[0]:= 2: q:= 3:

while count < N+1 do

  p:= q; q:= nextprime(p);

  for r from 1 to N do x:= -p mod P[r]; if subs(0=P[r], x) >= q-p then break fi od;

  r:= r-1;

  if r <= N and V[r] = 0 then V[r]:= p; count:= count+1;  fi;

od:

convert(V, list);

CROSSREFS

Cf. A341650.

Sequence in context: A146999 A147485 A341650 * A104189 A301776 A178570

Adjacent sequences:  A341637 A341638 A341639 * A341641 A341642 A341643

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, Feb 18 2021

STATUS

approved

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Last modified December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)