A056930 -id:A056930 - cp's OEIS frontend

A056929 Difference between n^2 and average of smallest prime greater than n^2 and largest prime less than n^2.

0, 0, 1, -1, 2, -1, 0, 0, 1, 1, 0, -1, 1, 0, 2, 1, 0, -2, 1, 0, 1, -3, 2, 0, 1, -1, 4, -5, 3, 1, -2, 0, -2, -1, 2, -1, 1, 4, 1, 0, -4, -5, -5, 3, -5, -1, 1, -4, 10, 0, 1, -2, 3, -5, 7, 9, -2, 1, 0, -2, 4, -9, 0, 1, 3, 1, -5, -10, 4, -4, 0, 1, 2, -6, 12, -4, 0, 3, -9, 3, -2, -2, 6, 1, -6, 2, -3

Offset: 2

Henry Bottomley, Jul 12 2000

Conjecture: the most frequent value will be 1 (including sequence variants with any even power n^2k). - Bill McEachen, Dec 12 2022

			a(4)=1 because smallest prime greater than 4^2 is 17, largest prime less than 4^2 is 13, average of 17 and 13 is 15 and 16-15=1.

Hugo Pfoertner, Table of n, a(n) for n = 2..10000

Cf. A007491, A053000, A053001, A056927, A056928, A056930, A056931.

with(numtheory): A056929 := n-> n^2-(prevprime(n^2)+nextprime(n^2))/2);

Array[# - Mean@ {NextPrime[#], NextPrime[#, -1]} &[#^2] &, 87, 2] (* Michael De Vlieger, May 20 2018 *)

a(n) = n^2 - (nextprime(n^2) + precprime(n^2))/2; \\ Michel Marcus, May 20 2018

a(n) = A000290(n) - A056928(n).

a(n) = (A056927(n) - A053000(n))/2.

More terms from James Sellers, Jul 13 2000

A056931 Difference between n-th oblong (promic) number, n(n+1), and the average of the smallest prime greater than n^2 and the largest prime less than (n+1)^2.

Original entry on oeis.org

0, 0, 0, 0, 0, -1, -1, 0, 3, -1, -2, -1, 0, 1, 2, 1, -3, -2, 0, 1, 1, -4, 2, -2, 0, 3, -1, 0, 0, -2, -3, 0, -3, 0, 0, 0, 3, 0, 5, -4, -6, -5, -3, 0, -6, 1, -2, 6, 2, -2, 1, -2, 0, 1, 9, 0, 2, -2, -3, 2, -1, -9, 1, 1, 2, -1, -6, -6, -1, -3, 0, 0, 0, 6, -1, -3, 3, -2, -7, 1, -2, 1, 2, -1, -4

Offset: 2

Henry Bottomley, Jul 12 2000

a(1)=-0.5 which is not an integer

			a(4)=0 because smallest prime greater than 4^2 is 17, largest prime less than 5^2 is 23, average of 17 and 23 is 20 and 4*5-20=0

Cf. A002378, A007491, A053000, A053001, A056927, A056928, A056929, A056930.

with(numtheory): A056931 := n-> n*(n+1)-(prevprime((n+1)^2)+nextprime(n^2))/2);

a(n) =A002378(n)-(A007491(n)+A053001(n+1))/2 =A002378(n)-A056930(n).

More terms from James Sellers, Jul 13 2000

A056928 Average of the smallest prime greater than n^2 and the largest prime less than n^2.

Original entry on oeis.org

4, 9, 15, 26, 34, 50, 64, 81, 99, 120, 144, 170, 195, 225, 254, 288, 324, 363, 399, 441, 483, 532, 574, 625, 675, 730, 780, 846, 897, 960, 1026, 1089, 1158, 1226, 1294, 1370, 1443, 1517, 1599, 1681, 1768, 1854, 1941, 2022, 2121, 2210, 2303, 2405, 2490

Offset: 2

Henry Bottomley, Jul 12 2000

			a(4)=15 because the smallest prime greater than 4^2 is 17, the largest prime less than 4^2 is 13, and the average of 17 and 13 is 15.

Hugo Pfoertner, Table of n, a(n) for n = 2..10000

Cf. A007491, A053000, A053001, A056927, A056929, A056930, A056931.

Table[n2=n^2;(NextPrime[n2,-1]+NextPrime[n2])/2,{n,2,100}] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)

a(n) = (nextprime(n^2) + precprime(n^2))/2; \\ Michel Marcus, May 20 2018

a(n) = (A007491(n) - A053001(n))/2.
a(n) = A000290(n) + (A053000(n) - A056927(n))/2.
a(n) = A000290(n) - A056929(n).

cp's OEIS Frontend

A056929 Difference between n^2 and average of smallest prime greater than n^2 and largest prime less than n^2.

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A056931 Difference between n-th oblong (promic) number, n(n+1), and the average of the smallest prime greater than n^2 and the largest prime less than (n+1)^2.

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A056928 Average of the smallest prime greater than n^2 and the largest prime less than n^2.

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