cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Daniel Drucker

Daniel Drucker's wiki page.

Daniel Drucker has authored 9 sequences.

A227828 a(0)=2; for n>0, a(n) is the smallest (odd or even) prime p such that the n-th prime p_n divides a(n-1)+p.

Original entry on oeis.org

2, 2, 7, 3, 11, 11, 2, 83, 31, 61, 113, 11, 137, 109, 149, 227, 197, 157, 331, 71, 71, 2, 709, 619, 271, 311, 1103, 751, 2459, 157, 521, 241, 283, 1087, 859, 631, 577, 1307, 1301, 2039, 37, 1753, 419, 727, 431, 751, 443, 401, 491, 2687, 61
Offset: 0

Views

Author

Daniel Drucker, Jul 21 2013

Keywords

Comments

Agrees with A227827 from a(8) on.

Crossrefs

Cf. A227826, A227827.

A227827 a(0)=3; for n>0, a(n) is the smallest (odd or even) prime p such that the n-th prime p_n divides a(n-1)+p.

Original entry on oeis.org

3, 3, 3, 2, 5, 17, 61, 7, 31, 61, 113, 11, 137, 109, 149, 227, 197, 157, 331, 71, 71, 2, 709, 619, 271, 311, 1103, 751, 2459, 157, 521, 241, 283, 1087, 859, 631, 577, 1307, 1301, 2039, 37, 1753, 419, 727, 431, 751, 443, 401, 491, 2687, 61
Offset: 0

Views

Author

Daniel Drucker, Jul 21 2013

Keywords

Comments

a(0) could be any odd prime - the rest of the sequence is unchanged.
Agrees with A227828 from a(8) on.

Crossrefs

Cf. A227826, A227828.

A227826 a(0)=3; for n>0, a(n) is the smallest odd prime p such that the n-th prime p_n divides a(n-1)+p.

Original entry on oeis.org

3, 3, 3, 7, 7, 37, 41, 61, 53, 131, 43, 19, 277, 379, 137, 239, 79, 157, 331, 71, 71, 367, 107, 59, 653, 317, 491, 127, 2441, 829, 1657, 883, 1213, 157, 677, 1409, 101, 1783, 173, 829, 3323, 257, 467, 1061, 97, 691, 503, 1607, 1069, 293, 1997
Offset: 0

Views

Author

Daniel Drucker, Jul 21 2013

Keywords

Comments

a(0) could be any odd prime - the rest of the sequence is unchanged.

Crossrefs

Cf. A227827, A227828.

A224238 Decimal expansion of speed of light in miles per hour.

Original entry on oeis.org

6, 7, 0, 6, 1, 6, 6, 2, 9, 3, 8, 4, 3, 9, 5, 1, 3, 2, 4, 2, 6, 6, 2, 8, 4, 8, 9, 6, 2, 0, 6, 1, 5, 6, 0, 4, 8, 6, 7, 5, 7, 3, 3, 7, 1, 5, 1, 0, 3, 7, 9, 3, 8, 4, 3, 9, 5, 1, 3, 2, 4, 2, 6, 6, 2, 8, 4, 8, 9, 6, 2, 0, 6, 1, 5, 6, 0, 4, 8, 6
Offset: 9

Views

Author

N. J. A. Sloane, Apr 13 2013, following a suggestion from Daniel Drucker

Keywords

Comments

The exact answer (by definition) is 3600*299792458/(5280*0.3048).
Has period 42 since a(17). - Jianing Song, Aug 08 2022

Examples

			670616629.38439513242662848962061560486757337151037938439513...

Crossrefs

Cf. A003678, A224236, A224237.

A224237 Decimal expansion of speed of light in miles per second.

Original entry on oeis.org

1, 8, 6, 2, 8, 2, 3, 9, 7, 0, 5, 1, 2, 2, 0, 8, 7, 0, 1, 1, 8, 5, 0, 7, 9, 1, 3, 7, 8, 3, 5, 0, 4, 3, 3, 4, 6, 8, 5, 4, 3, 7, 0, 4, 7, 6, 4, 1, 7, 7, 2, 0, 5, 1, 2, 2, 0, 8, 7, 0, 1, 1, 8, 5, 0, 7, 9, 1, 3, 7, 8, 3, 5, 0, 4, 3, 3, 4, 6, 8
Offset: 6

Views

Author

N. J. A. Sloane, Apr 13 2013, following a suggestion from Daniel Drucker

Keywords

Comments

The exact answer (by definition) is 299792458/(5280*0.3048) = 186282.3970512208701185...
Many people remember the approximation 186000.
Has period 42 since a(15). - Jianing Song, Aug 08 2022

Examples

			186282.39705122087011850791378350433468543704764177205122087...

Crossrefs

Cf. A003678, A224236.

A224236 Decimal expansion of speed of light in feet per second.

Original entry on oeis.org

9, 8, 3, 5, 7, 1, 0, 5, 6, 4, 3, 0, 4, 4, 6, 1, 9, 4, 2, 2, 5, 7, 2, 1, 7, 8, 4, 7, 7, 6, 9, 0, 2, 8, 8, 7, 1, 3, 9, 1, 0, 7, 6, 1, 1, 5, 4, 8, 5, 5, 6, 4, 3, 0, 4, 4, 6, 1, 9, 4, 2, 2, 5, 7, 2, 1, 7, 8, 4, 7, 7, 6, 9, 0, 2, 8, 8, 7, 1, 3
Offset: 9

Views

Author

N. J. A. Sloane, Apr 13 2013, following a suggestion from Daniel Drucker

Keywords

Comments

The exact value (by definition) is 299792458/0.3048.
Has period 42 since a(16). - Jianing Song, Aug 08 2022

Examples

			983571056.43044619422572178477690288713910761154855643044619...

Crossrefs

Cf. A003678, A224237.

A224223 a(0)=2; for n>0, a(n) = smallest prime not occurring earlier in the sequence such that a(n-1)+a(n) is a multiple of n^2. If no such prime exists, the sequence terminates.

Original entry on oeis.org

2, 3, 5, 13, 19, 31, 41, 449, 127, 197, 103, 139, 149, 1879, 277, 173, 83, 5119, 389, 1777, 223, 659, 1277, 839, 313, 937, 1091, 367, 1201, 5527, 773, 4993, 1151, 7561, 2843, 4507, 677, 4799, 977, 5107, 4493, 15679, 7253, 26029, 3011, 1039, 5309, 3527
Offset: 0

Views

Author

Daniel Drucker and N. J. A. Sloane, Apr 05 2013

Keywords

Comments

Is this sequence infinite and, if so, is it a permutation of the primes? The answers are probably Yes and No (7 has not appeared after 10000 terms). Compare A134204.

Links

Crossrefs

Cf. A134204, A224221, A224222, A224229.

A224222 a(0)=3; for n>0, a(n) is the smallest prime q not already in the sequence such that the n-th prime p(n) divides a(n-1)+q. If no such prime q exists, the sequence terminates.

Original entry on oeis.org

3, 5, 7, 13, 29, 37, 2, 83, 31, 61, 113, 11, 137, 109, 149, 227, 197, 157, 331, 71
Offset: 0

Views

Author

Daniel Drucker and N. J. A. Sloane, Apr 05 2013

Keywords

Comments

a(20) does not exist, so the sequence terminates. A134204 is a similar sequence for which the termination question is unresolved.

Examples

			After a(3)=13, to find a(4) we look for a prime q such that the fourth prime, 7, divides 13+q, and q=29 works, since 7 divides 13+29 = 42.
After a(19)=71 we look for a prime q such that p(20)=71 divides 71+q. The only candidate is q=71. Since it is already in the sequence, the sequence terminates.

Crossrefs

Cf. A134204, A224221.

A224221 a(0)=3; for n>0, a(n) is the smallest odd prime q not already in the sequence such that the n-th prime p(n) divides a(n-1)+q. If no such prime q exists, the sequence terminates.

Original entry on oeis.org

3, 5, 7, 13, 29, 37, 41, 61, 53, 131, 43, 19, 277, 379, 137, 239, 79, 157, 331, 71
Offset: 0

Views

Author

Daniel Drucker and N. J. A. Sloane, Apr 05 2013

Keywords

Comments

a(20) does not exist, so the sequence terminates. A134204 is a similar sequence for which the termination question is unresolved.

Examples

			After a(3)=13, to find a(4) we look for an odd prime q such that the fourth prime, 7, divides 13+q, and q=29 works, since 7 divides 13+29 = 42.
After a(19)=71 we look for an odd prime q such that p(20)=71 divides 71+q. The only candidate is q=71. Since 71 is already in the sequence, the sequence terminates.

Crossrefs

Cf. A134204, A224222.

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