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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 Harvey P. Dale, Table of n, a(n) for n = 1..200 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**p0: ....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 Adjacent sequences:  A257115 A257116 A257117 * A257119 A257120 A257121 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 August 2 15:03 EDT 2021. Contains 346428 sequences. (Running on oeis4.)