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A102019 Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) + 23 for n > 0. 1
0, 2, 5, 14, 69, 75, 13023, 60345 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that (140*10^n - 23)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

Numbers corresponding to terms <= 75 are certified primes.

a(9) > 10^5. - Robert Price, Apr 10 2015

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..8.

Makoto Kamada, Prime numbers of the form 155...553.

Index entries for primes involving repunits.

FORMULA

a(n) = A102936(n) - 1.

EXAMPLE

1553 is prime, hence 2 is a term.

MATHEMATICA

Flatten[Position[NestList[10#+23&, 13, 75], _?PrimeQ]]-1 (* Harvey P. Dale, Jul 21 2013 *)

Select[Range[0, 10000], PrimeQ[(140*10^# - 23)/9] &] (* _Robert Price, Apr 10 2015 *)

PROG

(PARI) a=13; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+23)

(PARI) for(n=0, 1500, if(isprime((140*10^n-23)/9), print1(n, ", ")))

CROSSREFS

Cf. A000533, A002275, A102936.

Sequence in context: A158095 A227365 A059958 * A216270 A214374 A284661

Adjacent sequences:  A102016 A102017 A102018 * A102020 A102021 A102022

KEYWORD

nonn,hard,more

AUTHOR

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

EXTENSIONS

a(7)-a(8) derived from A102936 by Robert Price, Apr 10 2015

STATUS

approved

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Last modified May 22 18:53 EDT 2019. Contains 323481 sequences. (Running on oeis4.)