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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.

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A301914 a(n) is the least k for which A301913(n) divides 3^k+2.

Original entry on oeis.org

1, 5, 2, 6, 16, 3, 9, 6, 23, 18, 43, 4, 60, 19, 79, 25, 68, 9, 28, 78, 32, 57, 158, 137, 75, 111, 7, 22, 69, 86, 188, 65, 85, 176, 75, 64, 18, 239, 191, 286, 116, 140, 340, 338, 257, 226, 65, 23, 51, 180, 30, 207, 201, 265, 131, 481, 94, 367, 58, 85, 79
Offset: 1

Views

Author

Luke W. Richards, Mar 28 2018

Keywords

Comments

Combined with A301913 and A301915 can be used to eliminate values of 3^k+2 from prime searches.

Examples

			A301913(1) = 5 and 5 divides 3^1+2 but not 3^0+2, so a(1)=1.
A301913(5) = 19 and 19 does not divide 3^k+2 for 0 <= k < 16, however 19 divides 3^16+2, so a(5)=16.

Links

Crossrefs

Cf. A301913, A301915.

Programs

  • Maple
    subs(FAIL=NULL,[seq( numtheory:-mlog(-2,3,ithprime(i)), i=3..100)]); # Robert Israel, May 04 2018

Extensions

Corrected by Robert Israel, May 04 2018

A301915 a(n) is the multiplicative order of 3, modulo A301913(n).

Original entry on oeis.org

4, 6, 5, 16, 18, 28, 30, 42, 52, 29, 78, 41, 88, 48, 100, 53, 112, 126, 65, 136, 138, 148, 162, 172, 89, 196, 198, 210, 222, 113, 232, 120, 125, 256, 268, 280, 282, 292, 316, 330, 168, 173, 352, 378, 388, 400, 204, 209, 146, 221, 448, 228, 460, 462, 233
Offset: 1

Views

Author

Luke W. Richards, Mar 28 2018

Keywords

Comments

The multiplicative order of x mod y is the least positive value of z for which x^z == 1 (mod y).
Note: This is the least value for which A301913(n) divides 3^(A301914(n) + k*A(n)) + 2 for every nonnegative integer k.

Examples

			a(1) = 4 because A301913(1) = 5 and the multiplicative order of 3 modulo 5 = 4.
Note: Given a(1) = 4 and A301914(1) = 5, every value of k that can be written as k = 5 + 5j (for a nonnegative integer j) is a multiple of A301913(1) = 5.
a(7) = 30 because A301913(7) = 31 and the multiplicative order of 3 modulo 31 = 4.
Note: Given a(7) = 9 and A301914(7) = 30, every value of k that can be written as k = 30 + 9j (for a nonnegative integer j) is a multiple of A301913(7) = 31.

Crossrefs

Cf. A301913, A301914.
Showing 1-2 of 2 results.

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