A101116
Values in A101115 which are records.
Original entry on oeis.org
0, 5, 9, 14, 15, 18, 19, 20, 22
Offset: 1
Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 02 2004
-
from sympy import isprime, nextprime
def agen(): # generator of tuple of terms of (A101116, A101117, A101118)
n, pn, record = 0, 1, -1
while True:
n += 1
pn = nextprime(pn)
s, c, found = str(pn), 0, True
while found:
found = False
for d in "123456789":
if isprime(int(d+s)):
s, c, found = d+s, c+1, True
break
if c > record:
record = c
yield record, pn, int(s)
g = agen()
print([next(g)[0] for n in range(1, 7)]) # Michael S. Branicky, Jun 24 2022
A101118
a(n) = the resulting prime generated when the process described in A101115 is applied to A101117(n).
Original entry on oeis.org
2, 612113, 5372126317, 4818372912366173, 21291981879276213799, 912733515196363393600307, 668334992181698187977197951, 231879245133561335194866134641, 933651219687395363156136052921903
Offset: 1
Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 02 2004
a(3) = 5372126317 because 5372126317 is the last prime that can be generated by successively prepending nonzero digits to A101117(3). A101117(3) is 7. A101116(3) indicates that 9 digits can be successively prepended to 7 generating a new prime each time. Doing so and giving preference to the smallest digit which meets the requirement, generates the following primes: 17, 317, 6317, 26317, 126317, 2126317, 72126317, 372126317, 5372126317.
A101117
a(n) = the first prime yielding the record value A101116(n).
Original entry on oeis.org
2, 3, 7, 73, 13799, 600307, 77197951, 4866134641, 36052921903
Offset: 1
Chuck Seggelin (seqfan(AT)plastereddragon.com), Dec 02 2004
a(6) = 600307 because 600307 is the first prime to which A101116(6) digits (18) can be prepended yielding a new prime each time (giving preference to the smallest digit which meets the requirement) - 600307, 3600307, 93600307, ..., 9912733515196363393600307.
A259848
Suffixes of 4818372912366173 (all primes).
Original entry on oeis.org
3, 73, 173, 6173, 66173, 366173, 2366173, 12366173, 912366173, 2912366173, 72912366173, 372912366173, 8372912366173, 18372912366173, 818372912366173, 4818372912366173
Offset: 1
.......................3
.......................73
.......................173
.......................6173
.......................66173
.......................366173
.......................2366173
.......................12366173
.......................912366173
.......................2912366173
.......................72912366173
.......................372912366173
.......................8372912366173
.......................18372912366173
.......................818372912366173
.......................4818372912366173
Showing 1-4 of 4 results.
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