A078883 - OEIS

A078883

Lesser member p of a twin prime pair such that p+1 is 3-smooth.

3, 5, 11, 17, 71, 107, 191, 431, 1151, 2591, 139967, 472391, 786431, 995327, 57395627, 63700991, 169869311, 4076863487, 10871635967, 2348273369087, 56358560858111, 79164837199871, 84537841287167, 150289495621631, 578415690713087, 1141260857376767

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OFFSET

1,1

LINKS

Ray Chandler, Table of n, a(n) for n = 1..62 (terms < 10^1000)

FORMULA

a(n) = A027856(n)-1 = A078884(n)-2.

EXAMPLE

A000040(20) = 71 and 71+1 = 72 = 2^3*3^2 = A003586(17) and 71+2 = 73 = A000040(21), therefore 71 is a term.

MATHEMATICA

seq[max_] := Select[Sort[Flatten[Table[2^i*3^j - 1, {i, 1, Floor[Log2[max]]}, {j, 0, Floor[Log[3, max/2^i]]}]]], And @@ PrimeQ[# + {0, 2}] &]; seq[2*10^15] (* Amiram Eldar, Aug 27 2024 *)

PROG

(Python)

from itertools import islice

from heapq import heappop, heappush

from sympy import isprime

def A078883_gen(): # generator of terms

yield from (3, 5)

h, hset = [2, 3], {2, 3}

while True:

m = heappop(h)

if isprime(m-1) and isprime(m+1):

yield m-1

for p in (4, 6, 9):

mp = m*p

if mp not in hset:

heappush(h, mp)

hset.add(mp)

A078883_list = list(islice(A078883_gen(), 50)) # Chai Wah Wu, Apr 04 2026

CROSSREFS

Cf. A000040, A001359, A014574, A003586, A027856, A078884.

Apart from initial terms, same as A059960.

Sequence in context: A216181 A101781 A101783 * A355901 A155990 A109556

Adjacent sequences: A078880 A078881 A078882 * A078884 A078885 A078886

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 11 2002

STATUS

approved