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A136296
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"Special augmented primes": primes p such that the decimal number 1p1 is divisible by p.
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2
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11, 13, 137, 9091, 909091, 5882353, 909090909090909091, 909090909090909090909090909091, 9090909090909090909090909090909090909090909090909091, 909090909090909090909090909090909090909090909090909090909090909091
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OFFSET
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1,1
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COMMENTS
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According to the Magma Calculator (http://magma.maths.usyd.edu.au/calc/), all nine terms given for this sequence are prime. - Jon E. Schoenfield, Aug 24 2009
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REFERENCES
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Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 61.
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LINKS
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EXAMPLE
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11371/137 = 83, an integer, so the prime 137 is a term.
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MATHEMATICA
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max=6; a={}; For[i=1, i<=10^max, i++, If[Mod[FromDigits[Join[{1}, IntegerDigits[Prime[i]], {1}]], Prime[i]] == 0, AppendTo[a, Prime[i]]]]; a (* Stefano Spezia, Mar 26 2023 *)
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PROG
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(PARI) A136296k(k) = { local(l, d, lb, ub); d=factor(10^(k+1)+1)[, 1]; l=[]; lb=10^(k-1); ub=10*lb; for(i=1, #d, if(d[i]>=lb&&d[i]<ub, l=concat(l, [d[i]]))); l} l=[]; for(i=1, 60, l=concat(l, A136296k(i))); l \\ Franklin T. Adams-Watters, Apr 23 2008
(Python)
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
for k in count(2):
t = 10**(k+1) + 1
d = [t//i for i in range(100, 10, -1) if t%i == 0]
yield from (di for di in d if isprime(di))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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