A078884 Greater member p of a twin prime pair such that p-1 is 3-smooth.

5, 7, 13, 19, 73, 109, 193, 433, 1153, 2593, 139969, 472393, 786433, 995329, 57395629, 63700993, 169869313, 4076863489, 10871635969, 2348273369089, 56358560858113, 79164837199873, 84537841287169, 150289495621633

Offset

1,1

Links

Ray Chandler, Table of n, a(n) for n = 1..62 (terms < 10^1000, first 56 terms from Robert Israel)

Formula

a(n) = A027856(n) + 1 = A078883(n) + 2.

Example

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

Maple

N:= 10^100:
sort(select(t -> isprime(t) and isprime(t-2),
[seq(seq(1+2^i*3^j, i=1..ilog2(floor(N/3^j))), j=0..floor(log[3](N)))])); # Robert Israel, May 14 2018

Mathematica

1 + Select[With[{n = 10^15}, Sort@ Flatten@ Table[2^p * 3^q, {p, 0, Log2@ n}, {q, 0, Log[3, n/(2^p)]}] ], AllTrue[# + {-1, 1}, PrimeQ] &] (* Michael De Vlieger, May 14 2018 *)

Prog

(Python)
from itertools import islice
from heapq import heappop, heappush
from sympy import isprime
def A078884_gen(): # generator of terms
    yield from (5, 7)
    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)
A078884_list = list(islice(A078884_gen(), 50)) # Chai Wah Wu, Apr 04 2026

Crossrefs

Cf. A006512, A014574, A003586, A027856.

Essentially the same as A060211.

Sequence in context: A129782 A080829 A224789 * A314328 A314329 A154872

Adjacent sequences: A078881 A078882 A078883 * A078885 A078886 A078887

Keyword

nonn

Author

Reinhard Zumkeller, Dec 11 2002

Status

approved