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A074924
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Numbers whose square is the sum of two successive primes.
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22
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6, 10, 12, 24, 42, 48, 62, 72, 84, 90, 110, 120, 122, 174, 204, 208, 220, 232, 240, 264, 306, 326, 336, 372, 386, 408, 410, 444, 454, 456, 468, 470, 474, 522, 546, 550, 594, 600, 630, 640, 642, 686, 740, 750, 762, 766, 788, 802, 852, 876, 882, 920, 936, 970
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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6^2 = 17 + 19, 1610^2 = 1296041 + 1296059.
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MATHEMATICA
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Select[Sqrt[#]&/@(Total/@Partition[Prime[Range[50000]], 2, 1]), IntegerQ] (* Harvey P. Dale, Oct 04 2014 *)
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PROG
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(PARI) select( {is_A074924(n)=!bittest(n=n^2, 0) && precprime(n\2)+nextprime(n\/2)==n}, [1..999]) \\ M. F. Hasler, Jan 03 2020
(PARI) A74924=[6]; apply( A074924(n)={while(n>#A74924, my(N=A74924[#A74924]); until( is_A074924(N+=2), ); A74924=concat(A74924, N)); A74924[n]}, [1..99]) \\ M. F. Hasler, Jan 03 2020
(Python)
from itertools import count, islice
from sympy import nextprime, prevprime
def agen(): # generator of terms
for k in count(4, step=2):
kk = k*k
if prevprime(kk//2+1) + nextprime(kk//2-1) == kk:
yield k
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CROSSREFS
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Square roots of squares in A001043.
Cf. A064397 (numbers n such that prime(n) + prime(n+1) is a square), A071220 (prime(n) + prime(n+1) is a cube), A074925 (n^3 is sum of 2 consecutive primes).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Crossrefs section corrected and extended by M. F. Hasler, Jan 03 2020
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STATUS
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approved
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