A142324 -id:A142324 - cp's OEIS frontend

A201820 Numbers k such that 90*k + 23 is prime.

0, 1, 3, 4, 6, 7, 8, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 25, 28, 29, 32, 34, 39, 40, 42, 45, 47, 50, 52, 53, 55, 57, 59, 63, 64, 67, 68, 70, 76, 78, 84, 85, 87, 90, 95, 96, 97, 99, 102, 103, 105, 108, 109, 110, 112, 113, 116, 119, 122, 123, 125, 129, 131

Offset: 1

J. W. Helkenberg, Dec 05 2011

This sequence was generated by adding 12 Fibonacci-like sequences. Looking at the format 90*k+23 modulo 9 and modulo 10 we see that all entries of A142324 have digital root 5 and last digit 3. (Reverting the process is an application of the Chinese remainder theorem.)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818.

[n: n in [0..200] | IsPrime(90*n+23)]; // Vincenzo Librandi, Dec 11 2011

Select[Range[0,400],PrimeQ[90 #+23]&] (* Vincenzo Librandi, Dec 11 2011 *)

is(n)=isprime(90*n+23) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A142324(n) - 23)/90.

A214360 Primes congruent to 23 modulo 3120613860.

Original entry on oeis.org

23, 3120613883, 6241227743, 9361841603, 12482455463, 15603069323, 18723683183, 21844297043, 24964910903, 28085524763, 34326752483, 43688594063, 62412277223, 115462712843, 124824554423, 156030693023, 159151306883, 171633762323, 180995603903, 196598673203

Offset: 1

Reinhard Zumkeller, Jul 13 2012

nonn

A211889(9) = 3120613860;

the first 10 terms constitute row 9 of triangle A211890, an arithmetic progression of 10 primes.

Cf. A010051.

Sequences of numbers congruent 23 modulo m: A134517 m=24, A141945 m=25, A140375 m=26, A141963 m=27, A141974 m=28, A141999 m=29, A132235 m=30, A142027 m=31, A142044 m=32, A142062 m=33, A142091 m=35, A142107 m=36, A142132 m=37, A142173 m=39, A142192 m=40, A142220 m=41, A142244 m=42, A142272 m=43, A142302 m=44, A142324 m=45, A142374 m=47, A142405 m=48, A142433 m=49, A142490 m=51, A142518 m=52, A142553 m=53, A142617 m=55, A142650 m=56, A142679 m=57, A142750 m=59, A142790 m=60, A142821 m=61, A142902 m=63, A142935 m=64, A140844 m=210.

a214360 n = a214360_list !! (n-1)
a214360_list = [x | k <- [0..], let x = 3120613860*k+23, a010051' x == 1]

select(isprime,[seq(23+i*3120613860,i=0..1000)]); # Robert Israel, Jun 07 2015

Select[Range[23, 2 10^11, 3120613860], PrimeQ] (* Vincenzo Librandi, Jun 07 2015 *)

is(n)=isprime(n) && n%3120613860==23 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 658414080n log n. - Charles R Greathouse IV, Jul 02 2016

cp's OEIS Frontend

A201820 Numbers k such that 90*k + 23 is prime.

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