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 A244282 Consider a prime number p with m decimal digits. The sequence lists the primes p such that the prefix of length m-1 and the suffix of length m-1 are both prime numbers. 3
 23, 37, 53, 73, 113, 131, 137, 173, 179, 197, 311, 313, 317, 373, 379, 419, 431, 479, 613, 617, 619, 673, 719, 797, 971, 1013, 1019, 1031, 1097, 1277, 1373, 1499, 1571, 1733, 1811, 1997, 2113, 2239, 2293, 2719, 3079, 3137, 3313, 3373, 3491, 3499, 3593, 3673, 3677, 3733 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let x(0)x(1)... x(q-1)x(q) denote the decimal expansion of a prime p. The sequence lists the primes p such that the prefix x(0)x(1)... x(q-1) and the suffix x(1)... x(q-1)x(q) are primes. Superset of A051362; a(n) first differs from A051362 when n=12. LINKS Paolo P. Lava, Table of n, a(n) for n = 1..1000 EXAMPLE The prime number 179 is in the sequence because 17 and 79 are primes. MAPLE with(numtheory): for m from 1 to 200 do: n:=ithprime(m):x:=convert(n, base, 10):n1:=nops(x): s1:=sum('x[i]*10^(i-1) ', 'i'=1..n1-1): s2:=(n-irem(n, 10))/10: if type(s1, prime)=true and type(s2, prime)=true then printf(`%d, `, n): else fi: od: MATHEMATICA Select[Prime[Range[1000]], (id = IntegerDigits[#]; PrimeQ[FromDigits[Take[id, {1, -2}]]] && PrimeQ[FromDigits[Take[id, {2, -1}]]]) &] (* César Eliud Lozada, Mar 31 2024 *) CROSSREFS Cf. A000040, A051362, A244283. Sequence in context: A063643 A361530 A057876 * A051362 A034302 A057878 Adjacent sequences: A244279 A244280 A244281 * A244283 A244284 A244285 KEYWORD nonn,base AUTHOR Michel Lagneau, Jun 25 2014 EXTENSIONS Inserted missing term a(49) and corrected a(50) by Paolo P. Lava, Dec 04 2017 STATUS approved

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Last modified September 18 02:51 EDT 2024. Contains 375995 sequences. (Running on oeis4.)