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 A256481 Smallest prime obtained by appending a number with identical digits to n or 0 if no such prime exists. 3
 2, 11, 23, 31, 41, 53, 61, 71, 83, 97, 101, 113, 127, 131, 149, 151, 163, 173, 181, 191, 2011, 211, 223, 233, 241, 251, 263, 271, 281, 293, 307, 311, 3299, 331, 347, 353, 367, 373, 383, 397, 401, 419, 421, 431, 443, 457, 461, 479, 487, 491, 503, 511111, 521, 5333 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS For n <= 15392, a(n) = 0 if and only if n = 6930. Conjecture: if a(n) = 0, then n is divisible by 3. Conjecture verified for n <= 10^6. a(n) = 0 for n = 6930, 50358, 56574, 72975. LINKS Chai Wah Wu, Table of n, a(n) for n = 0..6068 Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv:1503.08883 [math.NT], 2015. PROG (Python) from gmpy2 import mpz, digits, is_prime def A256481(n, limit=2000): ....if n in (6930, 50358, 56574, 72975): ........return 0 ....if n == 0: ........return 2 ....sn = str(n) ....for i in range(1, limit+1): ........for j in range(1, 10, 2): ............si = digits(j, 10)*i ............p = mpz(sn+si) ............if is_prime(p): ................return int(p) ....else: ........return 'search limit reached.' CROSSREFS Cf. A090287, A256480, A030665. Sequence in context: A106927 A158189 A218255 * A373225 A085745 A106856 Adjacent sequences: A256478 A256479 A256480 * A256482 A256483 A256484 KEYWORD nonn,base AUTHOR Chai Wah Wu, Mar 31 2015 STATUS approved

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Last modified August 10 21:39 EDT 2024. Contains 375058 sequences. (Running on oeis4.)