A069619
a(1) = 7; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and a(2n+1) = smallest prime ending in ( the least significant digits) a(2n-1). Alternate left and right concatenation yielding primes.
Original entry on oeis.org
7, 71, 271, 2711, 52711, 5271121, 135271121, 1352711219, 271352711219, 27135271121911, 1227135271121911, 122713527112191161, 20122713527112191161, 20122713527112191161109, 2720122713527112191161109
Offset: 1
a(4) = 2711 starting with a(3) = 271 and a(5) = 52711 in a(4) = 2711.
Cf.
A053582,
A069605,
A069606,
A069607,
A069608,
A069609,
A069610,
A069611,
A069613,
A069614,
A069615,
A069616,
A069617,
A069618.
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003
A069620
a(1) = 8; a(2n) = smallest prime that is a right concatenation of a(2n-1) and a number with no insignificant zeros and a(2n+1) = smallest prime ending in ( the least significant digits) a(2n-1). Alternate left and right concatenation yielding primes.
Original entry on oeis.org
8, 83, 283, 2833, 32833, 328331, 2328331, 232833127, 3232833127, 323283312749, 14323283312749, 1432328331274927, 281432328331274927, 28143232833127492741, 3628143232833127492741, 36281432328331274927411
Offset: 1
a(4) = 2833 starting with a(3) = 283 and a(5) = 32833 ending in a(4) = 2833.
Cf.
A053582,
A069605,
A069606,
A069607,
A069608,
A069609,
A069610,
A069611,
A069613,
A069614,
A069615,
A069616,
A069617,
A069618,
A069619.
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 30 2003
A236528
Start with 4; thereafter, primes obtained by concatenating to the end of previous term the next smallest number that will produce a prime.
Original entry on oeis.org
4, 41, 419, 41911, 4191119, 41911193, 419111933, 41911193341, 4191119334151, 419111933415151, 41911193341515187, 4191119334151518719, 419111933415151871963, 41911193341515187196323, 4191119334151518719632313, 419111933415151871963231329
Offset: 1
a(1) = 4 by definition.
a(2) is the next smallest prime beginning with 4, so a(2) = 41.
a(3) is the next smallest prime beginning with 41, so a(3) = 419.
...and so on.
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NestList[Module[{k=1},While[!PrimeQ[#*10^IntegerLength[k]+k],k+=2];#*10^IntegerLength[k]+ k]&,4,20] (* Harvey P. Dale, Jul 20 2024 *)
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import sympy
from sympy import isprime
def b(x):
num = str(x)
n = 1
while n < 10**3:
new_num = str(x) + str(n)
if isprime(int(new_num)):
print(int(new_num))
x = new_num
n = 1
else:
n += 1
b(4)
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