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A073945 Numbers n such that n + pi(n) is a square. 1
0, 1, 6, 11, 18, 27, 37, 49, 63, 114, 159, 183, 210, 238, 268, 299, 333, 368, 405, 443, 484, 526, 571, 663, 714, 765, 820, 874, 931, 990, 1049, 1110, 1176, 1241, 1307, 1380, 1451, 1523, 1598, 1673, 1834, 1916, 2001, 2174, 2266, 2355, 2544, 2643, 2737, 2837 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The corresponding sequence of squares is: 0,1,9,16,25,36,49,64,81,144,196,225,256,289,324,361,400,441,484,529,576,625,676,784,841,900,961,1024,1089,1156,1225,1296,1369,1444,1521,1600,1681,1764,1849,1936,... and the sequence of their square roots is: 0,1,3,4,5,6,7,8,9,12,14,15,16,17,18,19,20,21,22,23,24,25,26,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,46,47,48,50,51,52,54,55,56,57,58,59,60,61,62,63,64,65,66,68,69,70,....

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

EXAMPLE

Since pi(6)=3 and 6+3=9 is a square, so 6 belongs to the sequence.

MATHEMATICA

Select[Range[0, 3000], IntegerQ[Sqrt[#+PrimePi[#]]]&] (* Harvey P. Dale, Feb 01 2014 *)

PROG

(PARI) isok(n) = issquare(n + primepi(n)); \\ Michel Marcus, Feb 01 2014

CROSSREFS

Cf. A077510.

Sequence in context: A255654 A315564 A315565 * A083500 A102305 A160842

Adjacent sequences:  A073942 A073943 A073944 * A073946 A073947 A073948

KEYWORD

nonn

AUTHOR

David Garber, Nov 13 2002

EXTENSIONS

I put "more" to indicate that the two subsidiary sequences should be detached and made into separate sequences. - N. J. A. Sloane.

Offset changed and terms prepended by Harvey P. Dale and Michel Marcus, Feb 01 2014

STATUS

approved

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Last modified June 14 21:27 EDT 2021. Contains 345041 sequences. (Running on oeis4.)