A102991 -id:A102991

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A101726

Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) + 23 for n > 0.

+10
1

0, 3, 6, 18, 33, 53, 77, 89, 212, 306, 701, 1455, 2138, 2213, 3065, 9299, 16439, 16893, 28574, 54050

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Numbers n such that (410*10^n - 23)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

Numbers corresponding to terms <= 701 are certified primes.

a(21) > 10^5. Robert Price, May 08 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..20.

Makoto Kamada, Prime numbers of the form 455...553.

Index entries for primes involving repunits.

FORMULA

a(n) = A102991(n+1) - 1.

EXAMPLE

45553 is prime, hence 3 is a term.

MATHEMATICA

Select[Range[0, 300], PrimeQ[(410*10^# - 23)/9] &] (* Robert Price, May 08 2015 *)

PROG

(PARI) a=43; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+23)

(PARI) for(n=0, 1500, if(isprime((410*10^n-23)/9), print1(n, ", ")))

CROSSREFS

Cf. A000533, A002275, A102991.

KEYWORD

nonn,hard,more

AUTHOR

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

EXTENSIONS

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

a(17)-a(19) from Kamada data by Ray Chandler, Apr 30 2015

a(20) from Robert Price, May 08 2015

STATUS

approved

A177490

Primes of the form (41*10^n-23)/9.

+10
0

2, 43, 45553, 45555553, 45555555555555555553, 45555555555555555555555555555555553, 4555555555555555555555555555555555555555555555555555553

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..7.

MATHEMATICA

Select[(41 10^Range[0, 60]-23)/9, PrimeQ] (* Harvey P. Dale, Dec 12 2020 *)

PROG

(Magma) [a: n in [0..250] | IsPrime(a) where a is (41*10^n-23)div(9)]

CROSSREFS

Cf. A102991.

KEYWORD

nonn

AUTHOR

Vincenzo Librandi, Dec 11 2010

STATUS

approved

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