A101538 Indices of primes in sequence defined by A(0) = 63, A(n) = 10*A(n-1) + 53 for n > 0.

1, 2, 7, 49, 55, 71, 107, 131, 181, 1099, 1367, 1604, 5131, 22681

Offset

1,2

Comments

Numbers n such that (620*10^n - 53)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 8 followed by digit 3 is prime.

Numbers corresponding to terms <= 181 are certified primes.

a(15) > 10^5. - Robert Price, Sep 15 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..14.

Makoto Kamada, Prime numbers of the form 688...883.

Index entries for primes involving repunits.

Formula

a(n) = A103045(n) - 1.

Example

683 is prime, hence 1 is a term.

Mathematica

Flatten[Position[NestList[10#+53&, 63, 1700], _?(PrimeQ[#]&)]]-1 (* Harvey P. Dale, Sep 24 2013 *)

Prog

(PARI) a=63; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+53)
(PARI) for(n=0, 1500, if(isprime((620*10^n-53)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103045.

Sequence in context: A206153 A326338 A119668 * A045598 A293043 A186860

Adjacent sequences: A101535 A101536 A101537 * A101539 A101540 A101541

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

Status

approved