A335297 -id:A335297 - cp's OEIS frontend

A336585 Integers m such that (m-d)*(m+d) < (m-1)^2, where d is the smallest number such that both m-d and m+d are primes.

22, 28, 32, 38, 46, 49, 55, 58, 68, 74, 82, 87, 94, 112, 121, 128, 130, 136, 146, 155, 184, 200, 203, 206, 218, 221, 224, 238, 244, 247, 253, 265, 268, 284, 286, 301, 304, 306, 308, 316, 318, 320, 323, 326, 341, 344, 346, 362, 398, 412, 413, 428, 454, 466, 484

Offset: 1

Ya-Ping Lu, Oct 04 2020

nonn

All terms in this sequence are composites since, if m is a prime, d = 0 and (m-d)*(m+d) = m^2 > (m-1)^2.
It seems that the number of terms in this sequence is finite, with the last term being a(1225) = 1353559. Conjecture: there exist only 1225 semiprimes of the form (m-d)*(m+d), where d is the smallest number such that (m-d)*(m+d) < (m-1)^2.
a(n) in this sequence is the value of n in A047160 with m > sqrt(2*n - 1).
All terms <= 1353559 in A335297 can be found in this sequence.

			2 is not a term since for m = 2, d = 0 and (2-0)*(2-0) = 4 > (m-1)^2 = 1;
4 is not a term since for m = 4, d = 1 and (4-1)*(4+1) = 15 > (m-1)^2 = 9;
22 is a term since for m = 22, d = 9 and (22-9)*(22+9) = 403 < (m-1)^2 = 441;
1353559 is a term since for m = 1353559, d = 1722 and (1353559-1722)*(1353559+1722) = 1832119001197 < (m-1)^2 = 1832119259364.

Cf. A047160, A335297.

from sympy import isprime
n = 0
m = 2
while m >= 2:
    d = 0
    while d < m/2:
        p = m - d
        q = m + d
        if isprime(p) == 1 and isprime(q) == 1:
            if p*q < (m - 1) * (m - 1):
                n += 1
                print (m)
            break
        d += 1
    m += 1

cp's OEIS Frontend

A336585 Integers m such that (m-d)*(m+d) < (m-1)^2, where d is the smallest number such that both m-d and m+d are primes.

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