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 A256480 Smallest prime obtained by appending n to a nonzero number with identical digits or 0 if no such prime exists. 2
 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 211, 0, 113, 0, 0, 0, 317, 0, 419, 0, 421, 0, 223, 0, 0, 0, 127, 0, 229, 0, 131, 0, 233, 0, 0, 0, 137, 0, 139, 0, 241, 0, 443, 0, 0, 0, 347, 0, 149, 0, 151, 0, 353, 0, 0, 0, 157, 0, 359, 0, 461, 0, 163, 0, 0, 0, 167, 0, 269 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = 0 if n is even or a multiple of 5. Conjecture: all other terms are nonzero. Conjecture verified for n <= 10^7. "Appending" means "on the right". LINKS Chai Wah Wu, Table of n, a(n) for n = 0..10000 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 digits, mpz, is_prime def A256480(n, limit=2000): ....sn = str(n) ....if not (n % 2 and n % 5): ........return 0 ....for i in range(1, limit+1): ........for j in range(1, 10): ............si = digits(j, 10)*i ............p = mpz(si+sn) ............if is_prime(p): ................return int(p) ....else: ........return 'search limit reached.' CROSSREFS Cf. A090287, A256481. Sequence in context: A338827 A055963 A127805 * A088621 A088623 A167166 Adjacent sequences: A256477 A256478 A256479 * A256481 A256482 A256483 KEYWORD nonn,base AUTHOR Chai Wah Wu, Mar 31 2015 STATUS approved

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Last modified July 14 12:35 EDT 2024. Contains 374318 sequences. (Running on oeis4.)