A097954 -id:A097954 - cp's OEIS frontend

A274676 Numbers k such that 7*10^k + 13 is prime.

1, 3, 9, 12, 18, 19, 36, 37, 49, 67, 337, 893, 1924, 8044, 11610, 13560, 18777, 35376, 53601, 56022, 66488, 89801, 190210

Offset: 1

Vincenzo Librandi, Jul 03 2016

a(15) > 10000. - Felix Fröhlich, Jul 03 2016

			3 is in this sequence because 7*10^3 + 13 = 7013 is prime.
4 is not in the sequence because 7*10^4 + 13 = 70013 = 53 * 1321.
Initial terms and associated primes:
a(1) =  1: 83;
a(2) =  3: 7013;
a(3) =  9: 7000000013;
a(4) = 12: 7000000000013, etc.

Makoto Kamada, Search for 70w13.

Cf. numbers k such that 7*10^k + m is prime: A056804 (m=1), A097970 (m=3), A097954 (m=9), this sequence (m=13), A274677 (m=19), A274678 (m=27), A111021 (m=31), A274679 (m=33), A274700 (m=37), A274692 (m=43), A270974 (m=57).

[n: n in [1..800] | IsPrime(7*10^n+13)];

select(t -> isprime(7*10^t+13), [$1..2000]); # Robert Israel, Jul 03 2016

Select[Range[0, 3000], PrimeQ[7 * 10^# + 13] &]

is(n) = ispseudoprime(7*10^n+13) \\ Felix Fröhlich, Jul 03 2016

lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+13), print1(n, ", "))); \\ Altug Alkan, Jul 03 2016

a(15) from Michael S. Branicky, Jan 22 2023
a(16)-a(17) from Michael S. Branicky, Apr 10 2023
a(18)-a(23) from Kamada data by Tyler Busby, Apr 15 2024

A101130 Indices of primes in sequence defined by A(0) = 79, A(k) = 10*A(k-1) - 81 for k > 0.

Original entry on oeis.org

0, 1, 3, 5, 10, 11, 12, 34, 45, 56, 127, 155, 262, 352, 395, 428, 782, 981, 1057, 1562, 1694, 1815, 1936, 4235, 4430, 6857, 9897, 13144, 16645, 20890, 63350, 105295, 113692, 121143, 163779, 234914, 284750

Offset: 1

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

Numbers k such that 70*10^k + 9 is prime.
Numbers k such that digit 7 followed by k >= 0 occurrences of digit 0 followed by digit 9 is prime.
Numbers corresponding to terms <= 981 are certified primes.
a(38) > 3*10^5. - Robert Price, Jul 10 2023

			70009 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 700...009.
Index entries for primes involving repunits.

Cf. A000533, A002275, A097954.

[n: n in [0..400] |IsPrime(70*10^n + 9)]; // Vincenzo Librandi, Sep 06 2015

Select[Range[0, 300], PrimeQ[70*10^# + 9] &] (* Robert Price, Sep 05 2015 *)

a=79;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-81)

for(n=0,1500,if(isprime(70*10^n+9),print1(n,",")))

a(n) = A097954(n) - 1.

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(28)-a(31) from Kamada data by Ray Chandler, Apr 29 2015
a(32)-a(35) from Robert Price, Sep 05 2015
a(36)-a(37) from Robert Price, Jul 10 2023

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A274676 Numbers k such that 7*10^k + 13 is prime.

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A101130 Indices of primes in sequence defined by A(0) = 79, A(k) = 10*A(k-1) - 81 for k > 0.

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