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 A289829 Perfect squares of the form prime(k+1)^2 - prime(k)^2 + 1 where prime(k) is the k-th prime number. 1
 25, 49, 121, 169, 289, 361, 841, 961, 1681, 1849, 2401, 2809, 3721, 5929, 6889, 7921, 8281, 10201, 11449, 11881, 14161, 14641, 17689, 24649, 26569, 32041, 38809, 41209, 43681, 44521, 61009, 63001, 69169, 76729, 80089, 85849, 89401, 94249, 96721, 97969, 108241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 EXAMPLE 7^2 - 5^2 + 1 = 5^2, 17^2 - 13^2 + 1 = 11^2, 47^2 - 43^2 + 1 = 19^2, etc. MATHEMATICA TakeWhile[#, # < 110000 &] &@ Union@ Select[Array[Prime[# + 1]^2 - Prime[#]^2 + 1 &, 10^4], IntegerQ@ Sqrt@ # &] (* Michael De Vlieger, Jul 13 2017 *) PROG (Python) from __future__ import division from sympy import divisors, isprime, prevprime, nextprime A289829_list = [] for n in range(10**4):     m = n**2-1     for d in divisors(m):         if d*d >= m:             break         r = m//d         if not r % 2:             r = r//2             if not isprime(r):                 p, q = prevprime(r), nextprime(r)                 if m == (q-p)*(q+p):                     A289829_list.append(n**2)                     break # Chai Wah Wu, Jul 15 2017 (PARI) is(n) = if(!issquare(n), return(0), my(p=2); while(1, if(n==nextprime(p+1)^2-p^2+1, return(1)); p=nextprime(p+1); if(p > n, return(0)))) \\ Felix FrÃ¶hlich, Jul 15 2017 CROSSREFS Sequence in context: A106564 A308177 A104777 * A131706 A110015 A110586 Adjacent sequences:  A289826 A289827 A289828 * A289830 A289831 A289832 KEYWORD nonn AUTHOR Joseph Wheat, Jul 12 2017 EXTENSIONS More terms from Alois P. Heinz, Jul 13 2017 STATUS approved

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Last modified August 10 06:08 EDT 2022. Contains 356029 sequences. (Running on oeis4.)