A102953 -id:A102953 - cp's OEIS frontend

A101958 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) + 13 for n > 0.

0, 3, 6, 11, 29, 93, 177, 195, 563, 1800, 3519, 3537, 8232, 35160, 37404, 42329, 70050, 90791

Offset: 1

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

Numbers n such that (220*10^n - 13)/9 is prime.
Numbers n such that digit 2 followed by n >= 0 occurrences of digit 4 followed by digit 3 is prime.
Numbers corresponding to terms <= 563 are certified primes.
With changed signs, expansion of sinh(atan(x)).
Next term after 3537 is greater than 5000. - Ryan Propper, Jun 16 2005
a(19) > 10^5. - Robert Price, Mar 16 2015

			24443 is prime, hence 3 is a term.

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Makoto Kamada, Prime numbers of the form 244...443.
Index entries for primes involving repunits.

Cf. A000533, A002275, A102953.

a=23;for(n=0,2000,if(isprime(a),print1(n,","));a=10*a+13)

for(n=0,2000,if(isprime((220*10^n-13)/9),print1(n,",")))

a(n) = A102953(n) - 1.

2 more terms from Ryan Propper, Jun 16 2005
8232 from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007
a(14)-a(18) derived from A102953 by Robert Price, Mar 16 2015

A237257 Numbers k such that phi(k) = reversal(sigma(k)) - sigma(k).

Original entry on oeis.org

1863, 1979883, 126639495, 162037386, 1979999883, 1061283473946

Offset: 1

Giovanni Resta, Feb 05 2014

If p = (22*10^m - 13)/9 is prime, then 3^4*p is a term of the sequence. This happens for m = 1, 4, 7, 12, 30, 94, 178, 196, 564, ... .
a(7) > 3*10^12.
If k is in the sequence A102953 then p = (22*10^k - 13)/9 is prime. 9 divides all known terms; is it true for all terms of this sequence? - Farideh Firoozbakht, Feb 06 2014

			k = 1979999883 = 3^4*24444443 is a term, since sigma(k) = 2957777724 and 4277777592 - 2957777724 = 1319999868 = phi(k).

Cf. A102953, A230012.

cp's OEIS Frontend

A101958 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) + 13 for n > 0.

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