A101137 Indices of primes in sequence defined by A(0) = 71, A(n) = 10*A(n-1) + 21 for n > 0.

0, 2, 3, 4, 5, 8, 11, 30, 58, 68, 73, 286, 488, 591, 633, 1088, 1606, 3140, 5961, 6266, 9677, 11430, 12926, 32188, 38699, 53032, 83524, 185949

Offset

1,2

Comments

Numbers k such that (660*10^k - 21)/9 is prime.

Numbers k such that digit 7 followed by k >= 0 occurrences of digit 3 followed by digit 1 is prime.

Numbers corresponding to terms <= 633 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..28.

Makoto Kamada, Prime numbers of the form 733...331.

Index entries for primes involving repunits.

Formula

a(n) = A103055(n) - 1.

Example

7333331 is prime, hence 5 is a term.

Mathematica

Flatten[Position[NestList[10#+21&, 71, 2000], _?PrimeQ]]-1 (* Harvey P. Dale, Oct 03 2013 *)

Prog

(PARI) a=71; for(n=0, 1200, if(isprime(a), print1(n, ", ")); a=10*a+21)
(PARI) for(n=0, 1200, if(isprime((660*10^n-21)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103055.

Sequence in context: A210671 A189761 A329576 * A256386 A053021 A122700

Adjacent sequences: A101134 A101135 A101136 * A101138 A101139 A101140

Keyword

nonn,hard,more

Author

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

Extensions

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

a(24)-a(27) from Kamada data by Ray Chandler, Apr 30 2015

a(28) derived from A103055 by Elmo R. Oliveira, Dec 15 2025

Status

approved