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A062703 Squares that are the sum of two consecutive primes. 15
36, 100, 144, 576, 1764, 2304, 3844, 5184, 7056, 8100, 12100, 14400, 14884, 30276, 41616, 43264, 48400, 53824, 57600, 69696, 93636, 106276, 112896, 138384, 148996, 166464, 168100, 197136, 206116, 207936, 219024, 220900, 224676, 272484, 298116 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harry J. Smith, Table of n, a(n) for n=1..100

FORMULA

a(n) = A074924(n)^2.

a(n) = A000040(i) + A000040(i+1) with i = A064397(n) = A000720(A061275(n)). - M. F. Hasler, Jan 03 2020

EXAMPLE

prime(7) + prime(8) = 17 + 19 = 36 = 6^2.

MATHEMATICA

PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; f[n_] := Block[{m = Floor[n/2]}, s = PrevPrim[m] + NextPrim[m]; If[s == n, True, False]]; Select[ Range[550], f[ #^2] &]^2

t := Table[Prime[n] + Prime[n + 1], {n, 15000}]; Select[t, IntegerQ[Sqrt[#]] &] (* Carlos Eduardo Olivieri, Feb 25 2015 *)

PROG

(PARI) {for(n=1, 100, (p=precprime(n^2/2))+nextprime(p+2) == n^2 && print1(n^2", "))} \\ Zak Seidov, Feb 17 2011

(PARI) A062703(n)=A074924(n)^2 \\ M. F. Hasler, Jan 03 2020

CROSSREFS

Squares in A001043. See A226524 for cubes.

Cf. A074924 (square roots), A061275 (lesser of the primes), A064397 (index of that prime).

Cf. A080665 (same with sum of three consecutive primes).

Sequence in context: A296204 A063734 A069057 * A043438 A044223 A044604

Adjacent sequences:  A062700 A062701 A062702 * A062704 A062705 A062706

KEYWORD

easy,nonn

AUTHOR

Jason Earls, Jul 11 2001

EXTENSIONS

Edited by Robert G. Wilson v, Mar 02 2003

Edited (crossrefs completed, obsolete PARI code deleted) by M. F. Hasler, Jan 03 2020

STATUS

approved

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Last modified September 24 21:35 EDT 2020. Contains 337322 sequences. (Running on oeis4.)