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A257117 Smallest member of two consecutive prime numbers each of which is the sum of two squares. 3
37, 109, 193, 229, 277, 313, 349, 389, 397, 401, 449, 457, 509, 613, 661, 673, 701, 757, 761, 769, 797, 853, 929, 937, 997, 1009, 1093, 1109, 1193, 1201, 1213, 1237, 1373, 1429, 1489, 1549, 1597, 1609, 1637, 1669 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is a subset of A002313 (Primes of form x^2 + y^2).

LINKS

Abhiram R Devesh, Table of n, a(n) for n = 1..1000

EXAMPLE

a(1) =  37;  37 = (1*1) + (6*6)   ;  41 = (4*4) + (5*5).

a(2) = 109; 109 = (3*3) + (10*10) ; 113 = (7*7) + (8*8).

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)

....if a0!=0 and a1!=0:

........print(s0)

....s0=sympy.nextprime(s0)

CROSSREFS

Cf. A002313 (Primes of form x^2 + y^2).

Sequence in context: A142051 A282852 A171833 * A033215 A195316 A176549

Adjacent sequences:  A257114 A257115 A257116 * A257118 A257119 A257120

KEYWORD

nonn,easy

AUTHOR

Abhiram R Devesh, Apr 25 2015

STATUS

approved

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Last modified June 16 04:54 EDT 2019. Contains 324145 sequences. (Running on oeis4.)