A103274 -id:A103274 - cp's OEIS frontend

A285915 Integers n such that A112528(n) - A103274(n) = 1.

5, 7, 9, 12, 13, 16, 17, 19, 20, 22, 24, 25, 30, 32, 37, 38, 41, 47, 48, 52, 54, 57, 62, 63, 64, 67, 68, 73, 74, 75, 76, 78, 80, 81, 85, 87, 93, 94, 95, 96, 98, 101, 108, 109, 112, 115, 122, 124, 125, 126, 127, 128, 130, 131, 133, 134, 136, 137, 138, 140, 147

Offset: 1

Zak Seidov, Apr 28 2017

nonn

In general, A112528(n) - A103274(n) = 0 or 1.

Also, A000040(a(n)) = A063638(n).

Cf. A000040, A063638, A103274, A112528.

Select[Range@ 150, And[# != 1, PrimeOmega[Prime@ # - 2] == 2] &] (* Michael De Vlieger, May 01 2017 *)

is(n)=n!=1&&bigomega(prime(n)-2)==2 \\ David A. Corneth, Apr 29 2017

A342406 Primes p such that the number of ways to write p = 2*q + r with q and r prime is a prime.

Original entry on oeis.org

11, 13, 19, 23, 31, 41, 53, 59, 61, 67, 79, 89, 103, 139, 167, 179, 193, 199, 241, 251, 257, 277, 347, 367, 373, 409, 461, 463, 467, 479, 523, 541, 563, 601, 613, 641, 653, 691, 719, 743, 811, 823, 853, 881, 887, 937, 947, 977, 1039, 1063, 1087, 1117, 1129, 1151, 1223, 1249, 1259, 1277, 1283

Offset: 1

J. M. Bergot and Robert Israel, Mar 11 2021

nonn

Primes prime(k) such that A103274(k) is prime.

			a(3) = 19 because there are 2 ways: 19 = 2*3+13 = 2*7+5, and 2 is prime.

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A103274.

filter:= proc(p) local q, count;
  q:= 1; count:= 0;
  do
    q:= nextprime(q);
    if 2*q >= p then return isprime(count) fi;
    if isprime(p-2*q) then count:= count+1 fi
  od
end proc:
select(filter, [seq(ithprime(i),i=1..1000)]);

cp's OEIS Frontend

A285915 Integers n such that A112528(n) - A103274(n) = 1.

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