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A056245 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 31 for n > 0. 1
0, 5, 65, 1253, 8405, 67037 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that (130*10^n - 31)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 4 followed by digit 1 is prime.

Numbers corresponding to terms <= 1253 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

REFERENCES

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

LINKS

Table of n, a(n) for n=1..6.

Patrick De Geest, PDP Reference Table - 141.

Makoto Kamada, Prime numbers of the form 144...441.

Index entries for primes involving repunits.

FORMULA

a(n) = A082698(n-1) - 2 for n > 1.

EXAMPLE

1444441 is prime, hence 5 is a term.

MATHEMATICA

Select[Range[0, 2000], PrimeQ[(130 10^# - 31) / 9] &] (* Vincenzo Librandi, Nov 03 2014

PROG

(PARI) a=11; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+31)

(PARI) for(n=0, 1500, if(isprime((130*10^n-31)/9), print1(n, ", ")))

(MAGMA) [n: n in [0..500] | IsPrime((130*10^n-31) div 9)]; // Vincenzo Librandi, Nov 03 2014

CROSSREFS

Cf. A000533, A002275, A082698.

Sequence in context: A006278 A234871 A121822 * A195886 A079482 A147625

Adjacent sequences:  A056242 A056243 A056244 * A056246 A056247 A056248

KEYWORD

nonn,hard,more

AUTHOR

Robert G. Wilson v, Aug 18 2000

EXTENSIONS

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Edited by N. J. A. Sloane, Jun 15 2007

8405 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

Added one more term from the PDP table and updated a link, by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 04 2014

STATUS

approved

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Last modified July 20 12:37 EDT 2018. Contains 312804 sequences. (Running on oeis4.)