Original entry on oeis.org
1, 2, 6, 12, 24, 30, 42, 54, 60, 66, 90, 132, 138, 210, 270, 300, 318, 342, 390, 420, 450, 624, 690, 696, 750, 798, 924, 930, 1170, 1224, 1326, 1362, 1428, 1434, 1500
Offset: 1
As can be gathered from A127356, the first six records are A127356(1) = 1, A127356(2) = 2, A127356(3) = 6, A127356(10) = 12, A127356(13) = 24, A127356(77) = 30. Hence a(1) to a(6) are 1, 2, 6, 12, 24, 30.
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sk[n_]:=Module[{k=2},While[!PrimeQ[n+k^2],k=k+2];k];DeleteDuplicates[ Join[ {1},Table[sk[n],{n,Prime[Range[2,1000000]]}]],GreaterEqual] (* The program generates the first 22 terms of the sequence. *) (* Harvey P. Dale, Nov 07 2022 *)
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from itertools import count, islice
from sympy import isprime, nextprime, prime
def agen():
pn = 2; record = 1; yield record
for n in count(2):
k, pn = 2, nextprime(pn)
while not isprime(pn + k*k): k += 2
if k > record: record = k; yield record
print(list(islice(agen(), 20))) # Michael S. Branicky, Nov 11 2022
Original entry on oeis.org
1, 2, 3, 10, 13, 77, 92, 152, 294, 484, 517, 964, 1203, 2876, 14118, 34279, 81191, 103862, 115370, 195097, 334816, 347938, 2126572, 2787194, 3034023, 5707120, 16513290, 17861702, 19454321, 206814544, 500017558, 551865394, 716440254, 891826049, 1383516280
Offset: 1
The fifth record in A127356 is A129314(5) = 24 = A127356(13), hence a(5) = 13.
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from itertools import count, islice
from sympy import isprime, nextprime, prime
def agen():
pn = 2; record = 1; yield 1
for n in count(2):
k, pn = 2, nextprime(pn)
while not isprime(pn + k*k): k += 2
if k > record: record = k; yield n
print(list(islice(agen(), 20))) # Michael S. Branicky, Nov 11 2022
A309179
Primes to which a record size square needs to be added to reach another prime.
Original entry on oeis.org
2, 3, 5, 29, 41, 389, 479, 881, 1931, 3461, 3701, 7589, 9749, 26171, 153089, 405701, 1036829, 1354349, 1516829, 2677289, 4790309, 4990961, 34648631, 46214321, 50583209, 98999969, 305094851, 331498961, 362822099, 4373372351, 11037674441, 12239355719, 16085541359
Offset: 1
a(1) = 2; r(1) = 1.
a(2) = 3; 3 + 1^2 is composite, but 3 + 2^2 is prime, so r(2) = 2.
a(3) = 5; 5 + k^2 is composite for 0 < k < 6, but 5 + 6^2 is prime, so r(3) = 6.
The following are primes: 7 + 2^2, 11 + 6^2, 13 + 2^2, 17 + 6^2, 19 + 2^2, 23 + 6^2.
a(4) = 29; 29 + k^2 is composite for 0 < k < 12, but 29 + 12^2 is prime: r(4) = 12.
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f(n) = {k=1; while(!isprime(n+k^2), k++); k;}
lista(NN) = {m=0; forprime(p=1, NN, if(f(p)>m, m=f(p);print1(p,", ")))} \\ Jinyuan Wang, Jul 15 2019
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from sympy import isprime, nextprime
n, p, r = 0, 0, 0
while(True):
p = nextprime(p) ; k = 1
while not isprime(p + k**2):
k += 1
if k > r:
n += 1 ; r = k
print("a({}) = {}".format(n,p))
Showing 1-3 of 3 results.
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