A101140 Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) + 13 for n > 0.

0, 1, 18, 30, 105, 26193, 39972

Offset

1,3

Comments

Numbers n such that (670*10^n - 13)/9 is prime.

Numbers n such that digit 7 followed by n >= 0 occurrences of digit 4 followed by digit 3 is prime.

Numbers corresponding to terms <= 105 are certified primes.

The next term, if it exists, is bigger than 4000. - Stefan Steinerberger, Feb 04 2006

a(8) > 10^5. - Robert Price, Sep 25 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..7.

Makoto Kamada, Prime numbers of the form 744...443.

Index entries for primes involving repunits.

Formula

a(n) = A103058(n) - 1.

Example

73 is prime, hence 0 is a term.

Mathematica

For[n=0, n < 4000, n++, If[PrimeQ[(670*10^n - 13)/9], Print[n]]] (Steinerberger)

Prog

(PARI) a=73; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a+13)
(PARI) for(n=0, 1000, if(isprime((670*10^n-13)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103058.

Sequence in context: A043923 A160916 A091896 * A287683 A182254 A305220

Adjacent sequences: A101137 A101138 A101139 * A101141 A101142 A101143

Keyword

nonn,hard

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

Extensions

a(6) from Kamada data by Ray Chandler, Apr 30 2015

a(7) from Robert Price, Sep 25 2015

Status

approved