A212844 -id:A212844 - cp's OEIS frontend

A213085 First occurrence of n in A212844.

1, 7, 3, 5, 6, 9, 10, 55, 11, 3521, 246, 21, 52, 89969, 286, 60827, 22, 57481, 1501, 31937, 44, 2977, 49, 27, 40, 39806401, 110, 16777, 114, 214293, 24823, 247, 33, 259274569, 222, 2739, 70, 5993, 253217, 1062899, 72, 2007, 215, 85, 140, 4187, 50, 75

Offset: 0

Alex Ratushnyak, Jul 22 2012

nonn

It is conjectured that every integer n>=0 appears in A212844 at least once, and therefore every a(n) is defined.
Indices of terms that are bigger than 2^32-1 and possibly undefined: 69, 91, 114, 127, 141, 157, 175, 181, 195, 301, 313, 339, ...
Indices 69, 127, 175, 181, 301, 313, 339, ... correspond to terms that either do not exist or are greater than 2*10^12. - Charles R Greathouse IV, Aug 13 2015

			Smallest n such that A212844(n)=1 is 7, so a(1)=7.

Charles R Greathouse IV, Table of n, a(n) for n = 0..68

Cf. A212844, A213381, A213407.

a(n) = my(k=1); while(lift(Mod(2, k)^(k+2)) != n, k++); k; \\ Michel Marcus, Aug 14 2015

A112983 a(n) = 2^(n+1) mod n.

Original entry on oeis.org

0, 0, 1, 0, 4, 2, 4, 0, 7, 8, 4, 8, 4, 8, 1, 0, 4, 2, 4, 12, 16, 8, 4, 8, 14, 8, 25, 4, 4, 8, 4, 0, 16, 8, 1, 20, 4, 8, 16, 32, 4, 2, 4, 32, 34, 8, 4, 32, 11, 48, 16, 32, 4, 2, 31, 8, 16, 8, 4, 32, 4, 8, 16, 0, 64, 62, 4, 32, 16, 18, 4, 56, 4, 8, 61, 32, 36, 50, 4

Offset: 1

Paul Barry, Oct 08 2005

			a(3) = 2^4 mod 3 = 16 mod 3 = 1.

T. D. Noe, Table of n, a(n) for n = 1..10000

Cf. A106262, A212844.

[Modexp(2,n+1,n): n in [1..120]]; // G. C. Greubel, Jan 11 2023

Table[PowerMod[2, n + 1, n], {n, 100}] (* T. D. Noe, Aug 13 2012 *)

print([2**(n+1) % n for n in range(1,77)])
# Alex Ratushnyak, Aug 12 2012

[power_mod(2,n+1,n) for n in range(1,120)] # G. C. Greubel, Jan 11 2023

a(n) = A106262(2*n-1, n-2). - G. C. Greubel, Jan 11 2023

Name, data and offset corrected by Alex Ratushnyak, Aug 12 2012

A294389 a(n) = 2^(n-3) mod n, for n >= 3.

Original entry on oeis.org

1, 2, 4, 2, 2, 0, 1, 8, 3, 8, 10, 4, 1, 0, 13, 8, 5, 12, 1, 6, 6, 8, 4, 20, 10, 16, 22, 8, 8, 0, 1, 26, 11, 8, 28, 10, 1, 32, 31, 8, 11, 24, 19, 12, 12, 32, 16, 28, 1, 28, 40, 44, 26, 32, 1, 44, 15, 32, 46, 16, 1, 0, 4, 8, 17, 36, 1, 58, 18, 8, 55, 56, 46, 40, 60, 8, 20, 32, 10, 62, 21, 8, 4, 22

Offset: 3

Enrique Navarrete, Oct 29 2017

nonn

Every nonnegative integer seems to appear in the sequence, and every integer seems to appear in the sequence of first differences (see link).

For all 3 <= n < 10^9, a(n) != 7. - Robert G. Wilson v, Nov 30 2017

G. C. Greubel, Table of n, a(n) for n = 3..10000
Enrique Navarrete, Sequences Derived from Residues of 2^n (mod n)

Cf. A015910, A212844, A213859.

[Modexp(2,(n-3),n): n in [3..100]]; // G. C. Greubel, Jan 11 2023

Array[PowerMod[2, # - 3, #] &, 80, 3] (* Robert G. Wilson v, Nov 30 2017 *)

[power_mod(2,(n-3),n) for n in range(3,101)] # G. C. Greubel, Jan 11 2023

More terms from Robert G. Wilson v, Nov 30 2017

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A213085 First occurrence of n in A212844.

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A112983 a(n) = 2^(n+1) mod n.

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A294389 a(n) = 2^(n-3) mod n, for n >= 3.

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Magma

Mathematica

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