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A180134
Smallest k such that k*7^n is a sum of two successive primes.
9
5, 6, 18, 10, 30, 18, 4, 28, 4, 30, 30, 60, 120, 38, 12, 6, 52, 120, 70, 10, 102, 60, 70, 10, 186, 174, 42, 6, 90, 146, 154, 22, 18, 140, 20, 168, 24, 240, 60, 80, 26, 286, 154, 22, 12, 196, 28, 4, 2, 128, 116, 156, 422, 130, 204, 84, 12, 118, 88, 240, 536, 564, 798, 114
OFFSET
0,1
COMMENTS
If a(n) == 0 (mod 7), then a(n+1) = a(n)/7.
Records: 5, 6, 18, 30, 60, 120, 186, 240, 286, 422, 536, 564, 798, 1010, 1074, 1334, 1434, 1474, 3706, 4108, 4370, 6160, ..., .
Corresponding prime are twin primes for n = 0, 17, 369, ..., .
LINKS
MATHEMATICA
f[n_] := Block[{k = 1, j = 7^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 0]
PROG
(Python)
from sympy import isprime, nextprime, prevprime
def ok(n):
if n <= 5: return n == 5
return not isprime(n//2) and n == prevprime(n//2) + nextprime(n//2)
def a(n):
k, pow7 = 1, 7**n
while not ok(k*pow7): k += 1
return k
print([a(n) for n in range(64)]) # Michael S. Branicky, May 06 2021
KEYWORD
nonn
AUTHOR
STATUS
approved