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A077713
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a(1) = 3; thereafter a(n) = the smallest prime of the form d0...0a(n-1), where d is a single digit, or 0 if no such prime exists.
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4
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3, 13, 113, 2113, 12113, 612113, 50612113, 1050612113, 6001050612113, 26001050612113, 1026001050612113, 6000001026001050612113, 500006000001026001050612113, 600500006000001026001050612113, 1600500006000001026001050612113, 6001600500006000001026001050612113
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OFFSET
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1,1
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COMMENTS
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a(n) is the smallest prime obtained by prefixing a(n-1) with a number of the form d*10^k where d is a single digit, 0 < d < 10, and k >= 0. Conjecture: d*10^k always exists.
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LINKS
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EXAMPLE
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a(7) = 50612113: deleting 5 gives 612113 = a(6).
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MAPLE
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a:= proc(n) option remember; local k, m, d, p;
if n=1 then 3 else k:= a(n-1);
for m from length(k) do
for d to 9 do p:= k +d*10^m;
if isprime(p) then return p fi
od od
fi
end:
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PROG
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(Python)
from sympy import isprime
from itertools import islice
def agen(an=3):
while True:
yield an
pow10 = 10**len(str(an))
while True:
found = False
for t in range(pow10+an, 10*pow10+an, pow10):
if isprime(t):
an = t; found = True; break
if found: break
pow10 *= 10
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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