A336520 Primes in Pi: a(n) is the smallest prime factor of A090897(n) that does not appear in earlier terms of A090897, or 1, if no such factor exists.
3, 2, 53, 379, 58979, 161923, 2643383, 1746893, 6971, 5, 17, 1499, 11, 1555077581737, 297707, 4733, 37, 126541, 2130276389911155737, 1429, 71971, 383, 61, 1559, 29, 193, 12073, 698543, 157, 20289606809, 23687, 1249, 59, 2393, 251, 101, 15827173, 82351, 661
Offset: 1
Examples
[ 1] 3, {3} -> 3;
[ 2] 14, {2, 7} -> 2;
[ 3] 159, {3, 53} -> 53;
[ 4] 2653, {7, 379} -> 379;
[ 5] 58979, {58979} -> 58979;
[ 6] 323846, {2, 161923} -> 161923;
[ 7] 2643383, {2643383} -> 2643383;
[ 8] 27950288, {2, 1746893} -> 1746893;
[ 9] 419716939, {6971, 60209} -> 6971;
[10] 9375105820, {2, 5, 1163, 403057} -> 5.
Links
- Peter Luschny, Prime factorization for n = 1..100.
- David A. Corneth, Explanation of a method to determine the primality of a(n). Comes with example and PARI program.
Programs
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SageMath
def Select(item, Selected): return next((x for x in item if not (x in Selected)), 1) def PiPart(n): return floor(pi * 10^(n * (n + 1) // 2 - 1)) % 10^n def A336520List(len): prev = []; ret = [] for n in range(1, len + 1): p = prime_factors(PiPart(n)) ret.append(Select(p, prev)) prev.extend(p) return ret print(A336520List(39)) # Query function of David A. Corneth to determine if a(n) is prime. def LcmPiPart(n): return lcm([PiPart(n) for n in (1..n)]) def is_an_prime(n): lcmpi = LcmPiPart(n - 1) lm, m = 1, PiPart(n) while lm != m: lm, m = m, lcm(lcmpi, m) // lcmpi return m > 1
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