A091295 -id:A091295 - cp's OEIS frontend

A348193 (Number of primes == 3 mod 4 less than n^2) - (number of primes == 1 mod 4 less than n^2).

0, 1, 1, 1, 2, 2, 2, 1, 3, 2, 1, 3, 4, 3, 5, 5, 4, 3, 3, 3, 2, 3, 6, 6, 5, 5, 6, 4, 5, 5, 5, 5, 6, 4, 3, 3, 4, 3, 7, 12, 10, 7, 10, 8, 9, 10, 10, 7, 6, 6, 9, 8, 6, 6, 9, 6, 4, 9, 6, 8, 8, 7, 12, 11, 11, 9, 8, 9, 12, 9, 12, 17, 12, 13, 16, 12, 16, 18, 16, 15, 12, 12, 11, 17, 18, 14, 11, 13, 9, 5, 7, 7, 6, 7, 8, 7, 6, 8, 7, 10

Offset: 1

Seiichi Manyama, Oct 06 2021

a(790) = -1.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A014085, A077766, A077767, A091295, A348194, A348195, A348196.

a(n) = sum(k=2, n^2-1, (isprime(k)&&k%4==3)-(isprime(k)&&k%4==1));

a(n) = A348195(n) - A348196(n).

A093153 Difference between counts of odd composites in A093151 and A093152 [Count (1 mod 4) - count (3 mod 4)].

Original entry on oeis.org

0, 1, 6, 9, 24, 146, 217, 445, 550, 5959, 14251, 63336, 118471, 183456, 951699, 3458333, 6284059, 2581690, 80743227, 259753424

Offset: 1

Enoch Haga, Mar 24 2004

In A091295 the counts are 1 higher. I computed the differences through 10^8 and the rest by extrapolating from A091098 and A091099. In the ranges given, the counts of odd composites less than 10^n are higher 1 mod 4 than 3 mod 4. They are exactly opposite for the primes less than 10^n where 3 mod 4 is higher.

			Below 10^3 there are 169 odd composites 1 mod 4 and 163 odd composites 3 mod 4, so a(3)=169-163=6

Cf. A093151 A093152 A091295 A091098 A091099.

Subtract count of odd composites 3 mod 4 less than 10^n from those 1 mod 4

a(n) = A093151(n) - A093152(n). For n>1, a(n) = A091099(n) - A091098(n) - 1. [From Max Alekseyev, May 17 2009]

More terms from Max Alekseyev, May 17 2009

A093151 Number of odd composites 1 mod 4 less than 10^n.

Original entry on oeis.org

1, 13, 169, 1890, 20216, 210824, 2167819, 22119495, 224576508, 2272476724, 22940979719, 231196075659, 2326967290816, 23397529216327, 235077715264515, 2360380831212204, 23688221424314913, 237630022857420415, 2382971166402199310, 23889590198849417292

Offset: 1

Enoch Haga, Mar 24 2004

nonn

			Below 10^2 there are 13 odd composites so a(2)=13

Cf. A093152 A093153 A091295 A091098 A091099.

Count odd composites 1 mod 4 less than 10^n

For n>1, a(n) = 25*10^(n-2) - 1 - A091098(n). - Max Alekseyev, May 30 2007

More terms from Max Alekseyev, May 30 2007

Extended by Max Alekseyev, Oct 13 2009

A093152 Number of odd composites below 10^n that are congruent to 3 modulo 4.

Original entry on oeis.org

0, 12, 163, 1881, 20192, 210678, 2167602, 22119050, 224575958, 2272470765, 22940965468, 231196012323, 2326967172345, 23397529032871, 235077714312816, 2360380827753871, 23688221418030854, 237630022854838725, 2382971166321456083, 23889590198589663868

Offset: 1

Enoch Haga, Mar 24 2004

nonn

			Below 10^2 there are 12 odd composites 3 mod 4 so a(2)=12

Cf. A093151 A093153 A091295 A091098 A091099.

For n>1, a(n) = 25*10^(n-2) - A091099(n) [From Max Alekseyev, May 17 2009]

a(9) from Ryan Propper, Jun 21 2005

a(10)-a(20) from Max Alekseyev, May 17 2009, Oct 08 2013

A348194 a(n) = A077767(n) - A077766(n).

Original entry on oeis.org

1, 0, 0, 1, 0, 0, -1, 2, -1, -1, 2, 1, -1, 2, 0, -1, -1, 0, 0, -1, 1, 3, 0, -1, 0, 1, -2, 1, 0, 0, 0, 1, -2, -1, 0, 1, -1, 4, 5, -2, -3, 3, -2, 1, 1, 0, -3, -1, 0, 3, -1, -2, 0, 3, -3, -2, 5, -3, 2, 0, -1, 5, -1, 0, -2, -1, 1, 3, -3, 3, 5, -5, 1, 3, -4, 4, 2, -2, -1, -3, 0, -1, 6, 1, -4, -3, 2, -4, -4, 2, 0, -1, 1, 1, -1, -1, 2, -1, 3, 1, 2, -2, 5, 1, -1

Offset: 1

Seiichi Manyama, Oct 06 2021

sign

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A014085, A077766, A077767, A091295, A348193.

a(n) = sum(k=n^2, (n+1)^2, (isprime(k)&&k%4==3)-(isprime(k)&&k%4==1));

a(n) = A348193(n+1) - A348193(n).

cp's OEIS Frontend

A348193 (Number of primes == 3 mod 4 less than n^2) - (number of primes == 1 mod 4 less than n^2).

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A093153 Difference between counts of odd composites in A093151 and A093152 [Count (1 mod 4) - count (3 mod 4)].

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A093151 Number of odd composites 1 mod 4 less than 10^n.

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A093152 Number of odd composites below 10^n that are congruent to 3 modulo 4.

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A348194 a(n) = A077767(n) - A077766(n).

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