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 A347344 Positive integers k such that k with the first (most significant) digit repeated is prime. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 EXAMPLE 27 is a term because 227 is prime. MATHEMATICA upto=500; Select[Range[1, upto, 2], PrimeQ[FromDigits[Join[{First[d=IntegerDigits[#]]}, d]]]&] PROG (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 CROSSREFS Cf. A000040, A226099, A347343. Sequence in context: A298235 A111676 A058030 * A102498 A019399 A255581 Adjacent sequences: A347341 A347342 A347343 * A347345 A347346 A347347 KEYWORD nonn,base AUTHOR Paolo Xausa, Aug 27 2021 STATUS approved

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Last modified March 31 17:28 EDT 2023. Contains 361668 sequences. (Running on oeis4.)