A367075 a(n) is the least semiprime that is the first of n consecutive semiprimes s(1) ... s(n) such that s(i) - prime(i) are all equal.

4, 9, 118, 514, 1202, 9662, 46418, 198878, 273386, 717818, 717818, 270893786, 1009201118, 1009201118, 68668578806, 421210555538, 421210555538, 81550619289662, 645040014922382, 645040014922382, 645040014922382

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Example

a(3) = 118 because 118, 119, 121 are consecutive semiprimes with 118 - 2 = 119 - 3 = 121 - 5 = 116, and this is the first semiprime that works.

Maple

P:= select(isprime, [2, seq(i, i=3..10^6, 2)]):
SP:= select(t -> numtheory:-bigomega(t)=2, [$4..10^7]):
nSP:= nops(SP);
t:= 1: k0:= 1: R:= 4: tmax:= 1: d:= 2:
for k from 2 to nSP do
  if SP[k]-P[k-k0+1] = d then
    t:= t+1;
    if t > tmax then R:= R, SP[k0]; tmax:= t; fi;
  else
    t:= 1; k0:= k; d:= SP[k] - 2;
  fi
od:
R;

Crossrefs

All terms are in A001358 and (except for the initial term 4) A070552.

Sequence in context: A324024 A042381 A230743 * A033294 A156317 A115676

Adjacent sequences: A367072 A367073 A367074 * A367076 A367077 A367078

Keyword

nonn,more

Author

Robert Israel, Nov 05 2023

Extensions

a(12) from David A. Corneth, Nov 05 2023

a(13)-a(15) from Daniel Suteu, Nov 18 2023

a(16)-a(18) from Martin Ehrenstein, Dec 01 2023

a(19)-a(21) from Martin Ehrenstein, Dec 03 2023

Status

approved