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(PARI) a(n) = if ((n==1) || (n==3), 0, my(k=1); while (!isprime(eval(Str(k, prime(n)))), k++); k); \\ Michel Marcus, Jul 11 2021
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Subsidiary sequences: (set(1)) Index of the start of the first occurrence of a string of n consecutive 1's or 2's or 3's etc. (set (2)): a(n) = smallest prime such that concatenation of 1 with n successive primes starting from a(n) gives primes in each case. (n primes are obtained.) Similarly for 2, 3, etc. Conjecture: The subsidiary sequences are infinite. A065112(n) = a(n) concatenated with prime(n). - _Bill McEachen_, May 27 2021
A065112(n) = a(n) concatenated with prime(n). - Bill McEachen, May 27 2021
Subsidiary sequences: (set(1)) Index of the start of the first occurrence of a string of n consecutive 1's or 2's or 3's etc. (set (2)): a(n) = smallest prime such that concatenation of 1 with n successive primes starting from a(n) gives primes in each case. (n primes are obtained.) Similarly for 2, 3, etc. Conjecture: The subsidiary sequences are infinite. A065112(n) = a(n) concatenated with prime(n). - _Bill McEachen_, May 27 2021
The terms result from reverse concatenation of A065112(n) from prime(n), with the exception of primes 2 and 5. For example, the 47th prime is 211, and A065112(47) is "4" prefixed to 211 or 4211. The 47th term here (A088606) is the "4". Similarly, A065112(5) is "2" prefixed to the 5th prime (11) or 211, and the 5th term here is "2". - Bill McEachen, May 27 2021
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Subsidiary sequences: (set(1)) Index of the start of the first occurrence of a string of n consecutive 1's or 2's or 3's etc. (set (2)): a(n) = smallest prime such that concatenation of 1 with n successive primes starting from a(n) gives primes in each case. (n primes are obtained.) Similarly for 2, 3, etc. Conjecture: The subsidiary sequences are infinite.
The entries terms result from reverse concatenation of A065112(n) from prime(n), with the exception of primes 2 and 5. For example, the 47th prime is 211, and A065112(47) is "4" prefixed to 211 or 4211. The 47th entry term here (A088606) is the "4". Similarly, A065112(5) is "2" prefixed to the 5th prime (11) or 211, and the 5th entry term here is "2". - Bill McEachen, May 27 2021
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