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A255194 Numbers n such that prime(n) + {1,2,3,4,5,6} are all products of three primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 24 06:41 EST 2022. Contains 350534 sequences. (Running on oeis4.)