A202113 -id:A202113 - cp's OEIS frontend

A202115 Numbers n such that 90n + 17 is prime.

0, 1, 2, 5, 6, 7, 9, 12, 13, 14, 15, 18, 21, 22, 23, 25, 26, 27, 32, 35, 36, 37, 39, 40, 42, 46, 48, 50, 53, 54, 55, 57, 58, 60, 61, 65, 67, 70, 76, 77, 79, 81, 83, 84, 86, 88, 90, 92, 93, 97, 98, 104, 105, 111, 116, 123, 124, 127, 130, 131, 132, 133, 137

Offset: 1

J. W. Helkenberg, Dec 11 2011

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105, A202110, A202112, A202113, A202114.

select(t -> isprime(90*t+17),[$0..1000]); # Robert Israel, Sep 02 2014

Select[Range[0, 200], PrimeQ[90 # + 17] &]

is(n)=isprime(90*n+17) \\ Charles R Greathouse IV, Feb 20 2017

A202114 Numbers n such that 90n + 53 is prime.

Original entry on oeis.org

0, 2, 5, 6, 7, 8, 9, 10, 13, 16, 17, 24, 26, 29, 30, 31, 33, 35, 42, 43, 44, 47, 48, 49, 51, 52, 55, 58, 64, 65, 68, 69, 70, 75, 77, 80, 82, 83, 85, 86, 87, 91, 93, 94, 96, 97, 99, 103, 104, 112, 113, 114, 120, 124, 126, 127, 132, 134, 135, 138, 140, 141

Offset: 1

J. W. Helkenberg, Dec 11 2011

This sequence was generated by adding 12 Fibonacci-like sequences [See: PROG]. Looking at the format 90n+53 modulo 9 and modulo 10 we see that all entries of A142316 have digital root 8 and last digit 3. (Reverting the process is an application of the Chinese remainder theorem.) The 12 Fibonacci-like sequences are generated (via the p and q "seed" values entered into the PERL program) from the base p,q pairs 53*91, 19*17, 37*89, 73*71, 11*13, 29*67, 47*49, 83*31, 23*61, 41*43, 59*7, 77*79.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105, A202110, A202112, A202113.

Select[Range[0, 200], PrimeQ[90 # + 53] &]

is(n)=isprime(90*n+53) \\ Charles R Greathouse IV, Feb 20 2017

A202116 Numbers n such that 90n + 89 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 13, 15, 17, 18, 20, 21, 22, 25, 28, 29, 30, 31, 32, 36, 41, 44, 45, 46, 48, 51, 55, 58, 59, 62, 64, 65, 66, 69, 70, 72, 73, 77, 78, 83, 84, 86, 87, 88, 92, 97, 99, 105, 106, 107, 111, 112, 113, 116, 118, 119, 120, 121, 122, 123, 127, 129

Offset: 1

J. W. Helkenberg, Dec 11 2011

This sequence was generated by adding 12 Fibonacci-like sequences [See: PROG?]. Looking at the format 90n+89 modulo 9 and modulo 10 we see that all entries of A142335 have digital root 8 and last digit 9. (Reverting the process is an application of the Chinese remainder theorem.) The 12 Fibonacci-like sequences are generated (via the p and q "seed" values entered into the PERL program) from the base p,q pairs 89*91, 19*71, 37*17, 73*53, 11*49, 29*31, 47*67, 83*13, 23*43, 41*79, 59*61, 77*7.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105, A202110, A202112, A202113, A202114, A202115.

Select[Range[0, 200], PrimeQ[90 # + 89] &]

is(n)=isprime(90*n+89) \\ Charles R Greathouse IV, Jun 06 2017

A255512 Numbers k such that 60k+41, 90k+61 and 150*k+101 are all prime.

Original entry on oeis.org

0, 1, 4, 7, 21, 24, 31, 43, 46, 70, 99, 108, 109, 112, 154, 158, 176, 213, 218, 234, 238, 267, 273, 311, 319, 337, 381, 515, 518, 519, 528, 540, 658, 680, 689, 704, 736, 739, 752, 781, 837, 889, 1012, 1071, 1165, 1170, 1180, 1197, 1233, 1331, 1344, 1373, 1379

Offset: 1

Vincenzo Librandi, Feb 24 2015

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000
Umberto Cerruti, Pseudoprimi di Fermat e numeri di Carmichael (in Italian), p. 10.
Index entries for sequences related to Carmichael numbers.

Cf. A202113.

Cf. A255441 (Carmichael numbers of the form (60k+41)*(90k+61)*(150k+101)).

[n: n in [0..2000]| IsPrime(60*n+41) and IsPrime(90*n+61) and IsPrime(150*n+101)];

Select[Range[0, 1400], PrimeQ[60 # + 41] && PrimeQ[90 # + 61] && PrimeQ[150 # + 101] &]
Select[Range[0,1500],AllTrue[{60#+41,90#+61,150#+101},PrimeQ]&] (* Harvey P. Dale, Jan 13 2024 *)

is(k) = isprime(60*k + 41) && isprime(90*k + 61) && isprime(150*k + 101); \\ Amiram Eldar, Apr 24 2024

A202129 Numbers n such that 90n + 71 is prime.

Original entry on oeis.org

0, 2, 4, 5, 7, 9, 10, 11, 12, 16, 17, 20, 23, 26, 28, 31, 33, 35, 38, 39, 40, 41, 42, 46, 48, 49, 52, 54, 55, 59, 60, 62, 63, 66, 67, 72, 76, 77, 82, 83, 87, 89, 90, 101, 103, 104, 105, 108, 111, 112, 114, 117, 118, 119, 125, 126, 129, 133, 137, 138, 140

Offset: 1

J. W. Helkenberg, Dec 11 2011

This sequence was generated by adding 12 Fibonacci-like sequences [See: PROG?]. Looking at the format 90n+71 modulo 9 and modulo 10 we see that all entries of A142325 have digital root 8 and last digit 1. (Reverting the process is an application of the Chinese remainder theorem.) The 12 Fibonacci-like sequences are generated (via the p and q "seed" values entered into the Perl program) from the base p,q pairs 71*91, 19*89, 37*53, 73*13, 11*31, 29*49, 47*13, 83*67, 23*7, 41*61, 59*79, 77*43.

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820, A201822, A202101, A202104, A202105, A202110, A202112, A202113, A202114, A202115, A202116.

Select[Range[0, 200], PrimeQ[90 # + 71] &]

is(n)=isprime(90*n+71) \\ Charles R Greathouse IV, Jun 13 2017

A224860 Numbers n such that 90n + 59 and 90n + 61 are twin prime.

Original entry on oeis.org

0, 1, 2, 4, 6, 11, 13, 14, 21, 23, 25, 34, 36, 37, 43, 44, 51, 55, 56, 58, 62, 67, 69, 70, 71, 81, 93, 99, 102, 104, 112, 116, 120, 127, 132, 153, 155, 161, 169, 170, 188, 197, 200, 212, 242, 245, 252, 259, 265, 268, 279, 286, 291, 296, 298, 300, 302, 307

Offset: 1

J. W. Helkenberg, Jul 22 2013

All matching entries of A202101 and A202113 are twin prime.

Cf. A202101, A202113.

Select[Range[0, 499], PrimeQ[90# + 59] && PrimeQ[90# + 61] &]

More terms from Bruno Berselli, Jul 23 2013

cp's OEIS Frontend

A202115 Numbers n such that 90n + 17 is prime.

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A202114 Numbers n such that 90n + 53 is prime.

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A202116 Numbers n such that 90n + 89 is prime.

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A255512 Numbers k such that 60*k+41, 90*k+61 and 150*k+101 are all prime.

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A202129 Numbers n such that 90n + 71 is prime.

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A224860 Numbers n such that 90*n + 59 and 90*n + 61 are twin prime.

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A255512 Numbers k such that 60k+41, 90k+61 and 150*k+101 are all prime.

A224860 Numbers n such that 90n + 59 and 90n + 61 are twin prime.