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

Author

Robert Israel, Nov 05 2023

Keywords

• nonn
• more

Examples

			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.
		

Crossrefs

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

Programs

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;

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