A096774 -id:A096774 - cp's OEIS frontend

A100501 Numbers n such that 3*10^n+7 is prime.

1, 2, 5, 8, 24, 29, 84, 110, 129, 176, 593, 1137, 2675, 4992, 26904, 31572, 55077, 81021, 122274

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Nov 23 2004

593 and 1137 both give primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Sep 30 2005
a(19) > 10^5. - Robert Price, Jan 26 2015
a(20) > 2*10^5. - Robert Price, Jul 04 2015
Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

			(3*10^5)+7 = (3*100000)+7 = 300000+7 = 300007, which is prime.

Makoto Kamada, Prime numbers of the form 300...007.
Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Cf. A096774, A101824.

Do[ If[ PrimeQ[ 3*10^n + 7], Print[ n ]], {n, 0, 20000}]

is(n)=ispseudoprime(3*10^n+7) \\ Charles R Greathouse IV, May 22 2017

a(n) = A101824(n) + 1.

a(12) from Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 26 2004
a(13)-a(14) from Hugo Pfoertner, Nov 29 2004. The next term is > 20000.
a(15) from Kamada data by Robert Price, Dec 12 2010
a(16)-a(18) from Kamada data by Robert Price, Jan 26 2015
a(19) from Robert Price, Jul 04 2015

A100998 Indices of primes in sequence defined by A(0) = 97, A(n) = 10*A(n-1) - 63 for n > 0.

Original entry on oeis.org

0, 1, 2, 3, 4, 14, 18, 19, 45, 51, 52, 191, 379, 587, 775, 905, 1349, 1735, 2913, 7507, 15709, 16452, 17487, 18108, 21603, 25890, 26724, 34837, 67467

Offset: 1

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

Numbers n such that 90*10^n + 7 is prime.
Numbers n such that digit 9 followed by n >= 0 occurrences of digit 0 followed by digit 7 is prime.
Numbers corresponding to terms <= 1349 are certified primes.
a(30) > 2*10^5. - Robert Price, Oct 16 2015

			90007 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 900...007.
Index entries for primes involving repunits.

Cf. A000533, A002275, A096774.

Select[Range[0, 200000], PrimeQ[90*10^# + 7] &] (* Robert Price, Oct 16 2015 *)

a=97;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-63)

for(n=0,1500,if(isprime(90*10^n+7),print1(n,",")))

a(n) = A096774(n) - 1.

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

a(25)-a(29) from Kamada data by Ray Chandler, Apr 28 2015

cp's OEIS Frontend

A100501 Numbers n such that 3*10^n+7 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A100998 Indices of primes in sequence defined by A(0) = 97, A(n) = 10*A(n-1) - 63 for n > 0.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

Extensions