

A101073


Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n1)  31 for n > 0.


1



0, 1, 7, 16, 18, 24, 39, 48, 57, 58, 91, 112, 295, 636, 1855, 2514, 3592, 6990, 11839, 86071, 93507
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OFFSET

1,3


COMMENTS

Numbers n such that (770*10^n + 31)/9 is prime.
Numbers n such that digit 8 followed by n >= 0 occurrences of digit 5 followed by digit 9 is prime.
Numbers corresponding to terms <= 636 are certified primes.
a(22) > 10^5.  Robert Price, Oct 26 2015


REFERENCES

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462467.


LINKS

Table of n, a(n) for n=1..21.
Makoto Kamada, Prime numbers of the form 855...559.
Index entries for primes involving repunits.


FORMULA

a(n) = A103086(n)  1.


EXAMPLE

855555559 is prime, hence 7 is a term.


MATHEMATICA

Flatten[Position[NestList[10#31&, 89, 1000], _?PrimeQ]1] (* As written, the program will generate the first 14 terms of the sequence; changing the constant from 1000 to 7000 will generate 18 terms of the sequence but it will take a long time to do so *) (* Harvey P. Dale, Jul 16 2012 *)
Select[Range[0, 100000], PrimeQ[(770*10^# + 31)/9] &] (* Robert Price, Oct 26 2015 *)


PROG

(PARI) a=89; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a31)
(PARI) for(n=0, 1000, if(isprime((770*10^n+31)/9), print1(n, ", ")))


CROSSREFS

Cf. A000533, A002275, A103086.
Sequence in context: A193688 A132348 A177763 * A026226 A060914 A242917
Adjacent sequences: A101070 A101071 A101072 * A101074 A101075 A101076


KEYWORD

nonn,hard,more


AUTHOR

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwthaachen.de), Nov 30 2004


EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(19) from Kamada data by Ray Chandler, Apr 29 2015
a(20)a(21) from Robert Price, Oct 26 2015


STATUS

approved



