A243153 Larger of two consecutive primes whose difference is a semiprime.

11, 17, 23, 29, 37, 41, 47, 53, 59, 67, 71, 79, 83, 89, 101, 107, 113, 127, 131, 137, 149, 157, 163, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 277, 281, 293, 307, 311, 317, 331, 337, 347, 353, 359, 373, 379, 383, 389, 401, 419, 431, 439, 443

Offset: 1

Author

K. D. Bajpai, May 31 2014

Keywords

• nonn

Comments

Number of terms less than 10^k: 0, 0, 14, 107, 695, 4927, 37484, 295717, 2413153, ... - Muniru A Asiru, Jan 27 2018

Examples

			29 is prime and appears in the sequence because 29 - 23 = 6 = 2 * 3 which is a semiprime.
149 is prime and appears in the sequence because 149 - 139 = 10 = 2 * 5 which is a semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001358, A118590, A058620.

Programs

GAP

P := Filtered([1..10^4], IsPrime);;
P1 := List([1..Length(P)-1], i->P[i+1]-P[i]);;
P2:=[];; for i in [1..Length(P1)] do if Number(Factors(P1[i])) = 2 then Add(P2, P[i+1]); fi; od; A243153 := P2; # Muniru A Asiru, Jan 27 2018

Maple

with(numtheory): A243153:= proc()  ;if bigomega(ithprime(n+1)-ithprime(n))=2 then RETURN (ithprime(n+1)); fi; end: seq(A243153 (), n=1..200);

Mathematica

n = 0; Do[t = Prime[k] - Prime[k - 1]; If [PrimeOmega[t] == 2, n++; Print[n, " ", Prime[k]]], {k, 2, 25000}]
Select[Partition[Prime[Range[100]],2,1],PrimeOmega[#[[2]]-#[[1]]]==2&][[;;,2]] (* Harvey P. Dale, Mar 30 2025 *)