A103038 -id:A103038

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A101531

Indices of primes in sequence defined by A(0) = 61, A(n) = 10*A(n-1) + 41 for n > 0.

+10
1

0, 2, 3, 9, 21, 39, 53, 80, 83, 105, 192, 596, 680, 1362, 1875, 4023, 14162, 18732, 20841, 23727, 26418, 31449, 44693, 64766

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

OFFSET

1,2

COMMENTS

Numbers n such that (590*10^n - 41)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 5 followed by digit 1 is prime.

Numbers corresponding to terms <= 680 are certified primes.

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..24.

Makoto Kamada, Prime numbers of the form 655...551.

Index entries for primes involving repunits.

FORMULA

a(n) = A103038(n+1) - 1.

EXAMPLE

65551 is prime, hence 3 is a term.

MATHEMATICA

Select[Range[0, 100000], PrimeQ[(590*10^# - 41)/9] &] (* Robert Price, Sep 11 2015 *)

PROG

(PARI) a=61; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+41)

(PARI) for(n=0, 1500, if(isprime((590*10^n-41)/9), print1(n, ", ")))

CROSSREFS

Cf. A000533, A002275, A103038.

KEYWORD

nonn,hard,more

AUTHOR

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 06 2004

EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(17)-a(23) from Kamada data by Ray Chandler, Apr 30 2015

a(24) from Robert Price, Sep 11 2015

STATUS

approved

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