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A198019
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Primes occurring in the decimal expansion of Pi (A000796), ordered by position of last digit, then by size.
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6
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3, 31, 41, 5, 59, 4159, 14159, 314159, 2, 53, 653, 1592653, 89, 141592653589, 7, 97, 5897, 35897, 6535897, 5926535897, 415926535897, 79, 58979, 358979, 589793, 23, 9323, 9265358979323, 43, 643, 462643, 93238462643, 433, 83, 383, 2643383, 38462643383, 89793238462643383, 41592653589793238462643383
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OFFSET
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1,1
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COMMENTS
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Cf. A198018; the only difference is that here we list the "new primes" by increasing size (for a given subsequence of A000796).
Considering the first 1, 2, 3, 4,.... digits of the decimal expansion 3.14159... of Pi, record the primes that have not occurred earlier.
Sequence A198187 lists "duplicate" primes multiple times, each time they occur anew ending in another decimal place. - M. F. Hasler, Sep 01 2013
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LINKS
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EXAMPLE
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In Pi = 3... we have the prime a(1)=3.
In Pi = 3.1.... we have the prime a(2)=31.
In Pi = 3.14... we have no new prime.
In Pi = 3.141.... we have the prime a(3)=41.
In Pi = 3.1415.... we have the new prime a(5)=5.
In Pi = 3.14159.... we have the new primes (listed in increasing order) a(6)=59, a(7)=4159, a(8)=14159 and a(9)=314159. [M. F. Hasler, Sep 01 2013]
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PROG
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(PARI) {t=Pi; u=[]; for(i=0, precision(t), for(k=1, i+1, ispseudoprime(p=t\.1^i%10^k)& !setsearch(u, p)& (u=setunion(u, Set(p)))&print1(p", ")))}
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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