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A347344
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Positive integers k such that k with the first (most significant) digit repeated is prime.
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1
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1, 13, 23, 27, 29, 31, 37, 43, 49, 57, 61, 73, 81, 83, 87, 91, 97, 103, 109, 117, 123, 129, 151, 153, 163, 171, 181, 187, 193, 203, 207, 213, 221, 237, 239, 243, 251, 267, 269, 273, 281, 287, 293, 297, 301, 307, 313, 319, 323, 329, 331, 343, 347, 359, 361
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OFFSET
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1,2
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COMMENTS
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Conjecture: the sequence contains infinitely many twin prime pairs (k, k+2) such that (D(k), D(k+2)) is a twin prime pair, where D(x) = x with the most significant digit repeated. The first such k is 659: both (659, 661) and (6659, 6661) are twin prime pairs. All these k begin with either 3, 6, or 9.
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LINKS
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Michael S. Branicky, Table of n, a(n) for n = 1..10000
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EXAMPLE
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27 is a term because 227 is prime.
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MATHEMATICA
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upto=500; Select[Range[1, upto, 2], PrimeQ[FromDigits[Join[{First[d=IntegerDigits[#]]}, d]]]&]
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PROG
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(Python)
from sympy import isprime
def ok(n): s = str(n); return isprime(int(s[0] + s))
print(list(filter(ok, range(362)))) # Michael S. Branicky, Aug 27 2021
(PARI) isok(k) = my(d=digits(k)); isprime(eval(fromdigits(concat(d[1], d)))); \\ Michel Marcus, Sep 09 2021
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CROSSREFS
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Cf. A000040, A226099, A347343.
Sequence in context: A298235 A111676 A058030 * A102498 A019399 A255581
Adjacent sequences: A347341 A347342 A347343 * A347345 A347346 A347347
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KEYWORD
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nonn,base
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AUTHOR
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Paolo Xausa, Aug 27 2021
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STATUS
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approved
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