

A056892


a(n) = square excess of the nth prime.


18



1, 2, 1, 3, 2, 4, 1, 3, 7, 4, 6, 1, 5, 7, 11, 4, 10, 12, 3, 7, 9, 15, 2, 8, 16, 1, 3, 7, 9, 13, 6, 10, 16, 18, 5, 7, 13, 19, 23, 4, 10, 12, 22, 24, 1, 3, 15, 27, 2, 4, 8, 14, 16, 26, 1, 7, 13, 15, 21, 25, 27, 4, 18, 22, 24, 28, 7, 13, 23, 25, 29, 35, 6, 12, 18, 22, 28, 36, 1, 9, 19, 21
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OFFSET

1,2


LINKS

M. F. Hasler, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A053186(A000040(n)).
a(n) = A000040(n)  A000006(n)^2.  M. F. Hasler, Oct 04 2009


EXAMPLE

a(5) = 2 since the 5th prime is 11 = 3^2 + 2.
From M. F. Hasler, Oct 19 2018: (Start)
Written as a table, starting a new row when a square is reached, the sequence reads:
1, 2, // = 2  1, 3  1 = {primes between 1^2 = 1 and 2^2 = 4}  1
1, 3, // = 5  4, 7  4 = {primes between 2^2 = 4 and 3^2 = 9}  4
2, 4, // = 11  9, 13  9 = {primes between 3^2 = 9 and 4^2 = 16}  9
1, 3, 7, // = 17  16, 19  16, 23  16 = {primes between 16 and 25}  16
4, 6, // = 29  25, 31  25 = {primes between 5^2 = 25 and 6^2 = 36}  25
1, 5, 7, 11, // = {37, 41, 43, 47: primes between 6^2 = 36 and 7^2 = 49}  36
4, 10, 12, // = {53, 59, 61: primes between 7^2 = 49 and 8^2 = 64}  49
3, 7, 9, 15, // = {67, 71, 73, 79: primes between 8^2 = 64 and 9^2 = 81}  64
2, 8, 16, // = {83, 89, 97: primes between 9^2 = 81 and 10^2 = 100}  81
etc. (End)


MATHEMATICA

lst={}; Do[p=Prime[n]; s=p^(1/2); f=Floor[s]; a=f^2; d=pa; AppendTo[lst, d], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)
#Floor[Sqrt[#]]^2&/@Prime[Range[90]] (* Harvey P. Dale, Jul 06 2014 *)


PROG

(PARI) A056892(n)={my(p=prime(n)); psqrtint(p)^2} \\ M. F. Hasler, Oct 04 2009


CROSSREFS

Cf. A000040, A000196, A002496, A048760, A053186, A056893 .. A056898.
When written as a table, row lengths are A014085, and row sums are A108314  A014085 * A000290 = A320688.
Sequence in context: A023129 A007337 A167430 * A136523 A319855 A228731
Adjacent sequences: A056889 A056890 A056891 * A056893 A056894 A056895


KEYWORD

nonn


AUTHOR

Henry Bottomley, Jul 05 2000


STATUS

approved



