A365280 a(n) is the least number that starts a run of exactly n numbers that are members of A364462.

12, 324, 6252, 155673, 7445148, 457137900

Offset

1,1

Comments

A364462 contains arbitrarily long runs: for example, start with n coprime members t(1),...,t(n) of A365277 and use the Chinese Remainder Theorem to find k such that k == 1-i (mod t(i)) for i = 1 .. n.

Links

Table of n, a(n) for n=1..6.

Example

a(1) = 12 = 2^2 * 3 = prime(1) * prime(1) * prime(1+1) is in A364462.
a(2) = 324 = 2^2 * 3^4 is divisible by prime(1) * prime(1) * prime(1+1) and thus in A364462.
a(2) + 1 = 325 = 5^2 * 13 = prime(3) * prime(3) * prime(3+3).
a(3) = 6252 = 2^2 * 3 * 521 is divisible by  prime(1) * prime(1) * prime(1+1).
a(3) + 1 = 6253 = 13^2 * 37 = prime(6) * prime(6) * prime(6+6)
a(3) + 2 = 6254 = 2 * 53 * 49 = prime(1) * prime(16) * prime(17).
a(4) = 155673 = 3^2 * 7^2 * 353 is divisible by prime(2) * prime(2) * prime(2+2).
a(4) + 1 = 155674 = 2 * 277 * 281 = prime(1) * prime(59) * prime(1+59).
a(4) + 2 = 155675 = 5^2 * 13 * 479 is divisible by prime(3) * prime(3) * prime(3+3).
a(4) + 3 = 155676 = 2^2 * 3 * 12973 is divisible by 2 * 2 * 3 = prime(1) * prime(1) * prime(2).
a(5) = 7445148 = 2^2 * 3 * 620429 is divisible by 2 * 2 * 3 = prime(1) * prime(1) * prime(2).
a(5) + 1 = 7445149 = 41^2 * 43 * 103 is divisible by 41 * 43 * 103 = prime(13) * prime(14) * prime(27).
a(5) + 2 = 7445150 = 2 * 5^2 * 17 * 19 * 461 is divisible by 2 * 17 * 19 = prime(1) * prime(7) * prime(8).
a(5) + 3 = 7445151 = 3^2 * 7 * 59 * 2003 is divisible by 3 * 3 * 7 = prime(2) * prime(2) * prime(4).
a(5) + 4 = 7445152 = 2^5 * 11 * 13 * 1627 is divisible by 2 * 11 * 13 = prime(1) * prime(5) * prime(6).

Maple

filter:= proc(n) local F, i, j, m;
  F:= map(t -> `if`(t[2]>=2, numtheory:-pi(t[1])$2, numtheory:-pi(t[1])), ifactors(n)[2]);
  for i from 1 to nops(F)-1 do for j from 1 to i-1 do
    if member(F[i]+F[j], F) then return true fi
  od od;
  false
end proc:
V:= Vector(5): count:= 0: flag:= false:
for x from 1 while count < 5 do
  if filter(x) then
     if not flag then flag:= true; m:= x fi;
  elif flag then
     flag:= false; v:= x-m;
     if V[v] = 0 then count:= count+1; V[v]:= m; fi;
  fi
od:
convert(V, list);

Crossrefs

Cf. A364462, A365277.

Sequence in context: A083431 A239781 A288032 * A080141 A153468 A230817

Adjacent sequences: A365277 A365278 A365279 * A365281 A365282 A365283

Keyword

nonn,more

Author

Robert Israel, Aug 30 2023

Extensions

a(6) from David A. Corneth, Sep 01 2023

Status

approved