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A257118 Smallest of three consecutive prime numbers each of which is the sum of two squares. 2
89, 389, 397, 449, 661, 757, 761, 929, 997, 1193, 1201, 1669, 2213, 2269, 2293, 2593, 2609, 2617, 2741, 3037, 3041, 3209, 3217, 3413, 3433, 3449, 3697, 3877, 4397, 4801, 5189, 5233, 5237, 5569, 5689, 5717, 6101, 6217, 6389, 6469, 6733, 6829, 6833, 6997, 7529 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence is a subsequence of A257117.
LINKS
EXAMPLE
389 = 10^2 + 17^2, 397 = 6^2 + 19^2, and 401 = 1^2 + 20^2, so 389 is a term.
397 = 6^2 + 19^2, 401 = 1^2 + 20^2, and 409 = 3^2 + 20^2, so 397 is a term.
MATHEMATICA
Prime/@SequencePosition[Table[If[Count[IntegerPartitions[n, {2}], _?(AllTrue[ Sqrt[#], IntegerQ]&)]>0, 1, 0], {n, Prime[Range[3000]]}], {1, 1, 1}, Overlaps-> All] [[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 08 2018 *)
PROG
(Python)
import sympy
def sumpow(sn0, n, p):
....af=0; bf=0; an=1
....sn1=sn0+n
....if n!=0:
........sn1=sympy.nextprime(sn0, n)
....while an**p<sn1:
........bnsq=sn1-(an**p)
........bn=sympy.ntheory.perfect_power(bnsq)
........if bn!=False and list(bn)[1]==p:
............af=an
............bf=list(bn)[0]
............an=sn1+100
........an=an+1
....return(af, bf)
s0=1; pw=2
while s0>0:
....a0, b0=sumpow(s0, 0, pw)
....a1, b1=sumpow(s0, 1, pw)
....a2, b2=sumpow(s0, 2, pw)
....if a0!=0 and a1!=0 and a2!=0:
........print(s0)
....s0=sympy.nextprime(s0)
CROSSREFS
Cf. A064716 (Smallest member of three consecutive numbers).
Cf. A257117 (Smallest member of two consecutive prime numbers).
Sequence in context: A143828 A253140 A142448 * A244777 A107192 A061372
KEYWORD
nonn,easy
AUTHOR
Abhiram R Devesh, Apr 25 2015
EXTENSIONS
Corrected and extended by and prior b-file replaced by Harvey P. Dale, Jul 08 2018
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)