A181670 -id:A181670 - cp's OEIS frontend

A175036 a(n) = 2^(n-1) mod prime(n).

1, 2, 4, 1, 5, 6, 13, 14, 3, 19, 1, 13, 37, 22, 28, 14, 46, 44, 40, 24, 4, 18, 65, 2, 96, 10, 38, 31, 66, 2, 4, 124, 34, 82, 69, 32, 75, 103, 114, 5, 36, 78, 20, 6, 135, 125, 24, 132, 12, 13, 152, 24, 16, 8, 64, 218, 37, 55, 59, 170, 15, 270, 101, 104, 142, 185, 64, 16, 243, 28, 319, 12, 63, 308, 156, 252, 193, 334, 18, 159, 375, 298, 27, 316, 292, 65, 410, 220, 236, 173, 329, 46, 76, 150, 447, 46, 320, 118, 25, 17, 206, 399, 336, 457, 150, 3, 49, 116, 392, 512, 81, 77, 113, 75, 188, 50, 131, 116, 647, 63, 68

Offset: 1

Juri-Stepan Gerasimov, Dec 02 2010

nonn

Cf. A181670.

Table[PowerMod[2,n-1,Prime[n]],{n,200}] (* Zak Seidov, Dec 02 2010 *)

More terms from Zak Seidov, Dec 02 2010

A181615 Triangle read by rows: T(n,k) = 2^(n-1) mod semiprime(k).

Original entry on oeis.org

1, 2, 2, 0, 4, 4, 0, 2, 8, 8, 0, 4, 7, 6, 2, 0, 2, 5, 2, 4, 2, 0, 4, 1, 4, 8, 4, 1, 0, 2, 2, 8, 2, 8, 2, 18, 0, 4, 4, 6, 4, 1, 4, 14, 6, 0, 2, 8, 2, 8, 2, 8, 6, 12, 18, 0, 4, 7, 4, 2, 4, 16, 12, 24, 10, 1, 0, 2, 5, 8, 4, 8, 11, 2, 23, 20, 2, 8, 0, 4, 1, 6, 8, 1, 1, 4, 21, 14, 4

Offset: 1

Juri-Stepan Gerasimov, Dec 02 2010

			Triangle begins:
  1;
  2, 2;
  0, 4, 4;
  0, 2, 8, 8;
  0, 4, 7, 6, 2;
  ...

Cf. A173622, A181670.

Table[PowerMod[2, n-1, #[[;;n]]], {n, Length[#]}] & [Select[Range[50], PrimeOmega[#] == 2 &]] (* Paolo Xausa, Jun 29 2024 *)

trg(nn) = {semip = select(n->bigomega(n) == 2, vector(nn, i, i)); for (n = 1, #semip, for (k = 1, n, print1(2^(n-1) % semip[k], ", ");); print(););} \\ Michel Marcus, Sep 11 2013

Corrected by T. D. Noe, Dec 02 2010

A176041 Triangle read by rows: R(n, k) = 2^(2n - 2) mod prime(2k), 1<=k<=n.

Original entry on oeis.org

1, 1, 4, 1, 2, 3, 1, 1, 12, 7, 1, 4, 9, 9, 24, 1, 2, 10, 17, 9, 25, 1, 1, 1, 11, 7, 26, 11, 1, 4, 4, 6, 28, 30, 1, 7, 1, 2, 3, 5, 25, 9, 4, 28, 22, 1, 1, 12, 1, 13, 36, 16, 6, 27, 12, 1, 4, 9, 4, 23, 33, 21, 24, 47, 48, 9, 1, 2, 10

Offset: 1

Juri-Stepan Gerasimov, Dec 06 2010

The leftmost diagonal is all 1s because all even-indexed powers of 2 are congruent to 1 mod 3 (since 3 is the first even-indexed prime).

			Triangle begins:
1
1, 4
1, 2,  3
1, 1, 12,  7
1, 4,  9,  9, 24
1, 2, 10, 17,  9, 25
For example, R(4, 4) = 7 because 2^(2 * 4 - 2) = 2^6 = 64; the (2 * 4)th prime is 19; and 64 divided by 19 leaves a remainder of 7.

Cf. A000079, A181670.

ColumnForm[Table[Mod[2^(2n - 2), Prime[2k]], {n, 12}, {k, n}], Center]
Table[PowerMod[2,2n-2,Prime[2k]],{n,15},{k,n}]//Flatten (* Harvey P. Dale, Jul 15 2021 *)

cp's OEIS Frontend

A175036 a(n) = 2^(n-1) mod prime(n).

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A181615 Triangle read by rows: T(n,k) = 2^(n-1) mod semiprime(k).

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A176041 Triangle read by rows: R(n, k) = 2^(2n - 2) mod prime(2k), 1<=k<=n.

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Examples

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Programs

Mathematica