A255194 Numbers k such that prime(k) + {1,2,3,4,5,6} are all products of three primes.

369, 8788, 16456, 20522, 23335, 53601, 77047, 97930, 100123, 120745, 127847, 139723, 152996, 217177, 230179, 250248, 264618, 304656, 325478, 418592, 452277, 495518, 523028, 574110, 600888, 609574, 615102, 619844, 638584, 716516, 722010, 749479, 789769, 810082, 858158, 901322, 928090, 940735, 999329

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..5000

Example

prime(369) + {1,2,3,4,5,6} = {2522,2523,2524,2525,2526,2527} = {2*13*97, 3*29*29, 2*2*631, 5*5*101, 2*3*421, 7*19*19} - all products of 3 primes (A014612).

Mathematica

Reap[Do[If[Union[PrimeOmega[Prime[n] + {1, 2, 3, 4, 5, 6}]] == {3},
    Sow[n]], {n, 10^6}]][[2, 1]]

Prog

(Python)
from sympy import factorint, nextprime
A255194_list, p, p2 = [], 2, 3
for n in range(1, 10**6):
    if p2 - p > 6:
        for i in range(1, 7):
            fs = factorint(p+i)
            if len(fs) > 3 or sum(list(fs.values())) != 3:
                break
        else:
            A255194_list.append(n)
    p, p2 = p2, nextprime(p2) # Chai Wah Wu, Mar 01 2015

Crossrefs

Cf. A014612.

Sequence in context: A205903 A237844 A255202 * A108772 A224562 A276413

Adjacent sequences: A255191 A255192 A255193 * A255195 A255196 A255197

Keyword

nonn

Author

Zak Seidov, Feb 16 2015

Status

approved