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A062703 Squares that are the sum of two consecutive primes. 14
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.

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) je=[]; for(n=1, 39000, if(issquare(prime(n)+prime(n+1)), je=concat(je, prime(n)+prime(n+1)))); je

(PARI) { n=0; for (m=1, 10^9, if(issquare(a=prime(m) + prime(m + 1)), write("b062703.txt", n++, " ", a); if (n==100, break)) ) } \\ Harry J. Smith, Aug 09 2009

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

CROSSREFS

Cf. A080665.

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

STATUS

approved

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Last modified October 18 07:42 EDT 2019. Contains 328146 sequences. (Running on oeis4.)