A118590 -id:A118590 - cp's OEIS frontend

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

K. D. Bajpai, May 31 2014

nonn

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

			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.

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

Cf. A000040, A001358, A118590, A058620.

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

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

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 *)

A243155 Larger of the two consecutive primes whose positive difference is a cube.

Original entry on oeis.org

3, 97, 367, 397, 409, 457, 487, 499, 691, 709, 727, 751, 769, 919, 937, 991, 1117, 1171, 1201, 1381, 1447, 1531, 1567, 1579, 1741, 1831, 1987, 2011, 2161, 2221, 2251, 2281, 2467, 2539, 2617, 2671, 2707, 2749, 2851, 2887, 2917, 3019, 3049, 3217, 3229, 3457, 3499

Offset: 1

K. D. Bajpai, May 31 2014

nonn

Observation: All the terms in this sequence, after a(1), are the larger of the two consecutive primes which have positive difference either 2^3 or 4^3.

Superset of A031927 as the sequence contains for example numbers like 89753, 107441, 288647,.. (with gaps of 4^3...) that are not in A031927. - R. J. Mathar, Jun 06 2014

			97 is prime and appears in the sequence because 97 - 89 = 8 = 2^3.
397 is prime and appears in the sequence because 397 - 389 = 8 = 2^3.

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

Cf. A031927, A123996, A118590, A001632.

A243155:= proc() local a; a:=evalf((ithprime(n+1)-ithprime(n))^(1/3)); if a=floor(a) then RETURN (ithprime(n+1)); fi; end: seq(A243155 (), n=1..100);

n = 0; Do[t = Prime[k] - Prime[k - 1]; If[IntegerQ[t^(1/3)], n++; Print[n, " ", Prime[k]]], {k, 2, 15*10^4}]

s=[]; forprime(p=3, 4000, if(ispower(p-precprime(p-1), 3), s=concat(s, p))); s \\ Colin Barker, Jun 03 2014

cp's OEIS Frontend

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

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