

A198018


Yet unseen primes occurring within the first 1,2,3,4,... digits of Pi, A000796 (ordered according to position of last, then initial digit).


6



3, 31, 41, 5, 314159, 14159, 4159, 59, 2, 1592653, 653, 53, 141592653589, 89, 415926535897, 5926535897, 6535897, 35897, 5897, 97, 7, 358979, 58979, 79, 589793, 9265358979323, 9323, 23, 93238462643, 462643, 643, 43, 433, 41592653589793238462643383, 89793238462643383, 38462643383, 2643383, 383, 83
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OFFSET

1,1


COMMENTS

Consider the first, then the first two, then the first three, ..., terms of A000796, i.e., decimal digits of Pi. Look whether the concatenation of a certain number of subsequent digits yields a prime which did not yet occur earlier (and thus necessarily involves the last of the considered digits). If so, add this prime to the sequence.
Contains A005042 as a subsequence.


LINKS

Table of n, a(n) for n=1..39.


EXAMPLE

The first digit of the sequence is the prime a(1)=3.
The first two digits, "3.1", yield the prime a(2)=31.
In "3.14" there are no more primes. In "3.141" there is the prime a(3)=41.
In "3.1415" there is the prime a(4)=5.
In "3.14159" we have the primes 314159, 14159, 4159 and 59.


PROG

(PARI) {seen=[]; for(i=1, #PI1, for(j=1, i, isprime(p=eval(concat(vecextract(PI, Str(j".."i))))) & !setsearch(seen, p) & !print1(p", ") & seen=setunion(seen, Set(p))))}


CROSSREFS

Cf. A198019 ("new" primes ordered w.r.t. their size instead of starting position).
Cf. A047658.
Sequence in context: A090151 A198187 A198019 * A211003 A068331 A177104
Adjacent sequences: A198015 A198016 A198017 * A198019 A198020 A198021


KEYWORD

nonn,base,dumb


AUTHOR

M. F. Hasler, Oct 20 2011


STATUS

approved



