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 A158796 Index of first of three successive primes which sum to a cube. 3
 85, 3696, 79700, 263166, 283353, 434935, 678277, 950264, 1043678, 1266169, 1321463, 1436753, 2629623, 3568796, 3604676, 3676738, 3713180, 5096401, 5558697, 7162624, 9303565, 9504536, 10988577, 12778681, 13108392, 18730119 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..1000 EXAMPLE a(1)=85 because prime(85)+prime(86)+prime(87)=439+443+449=11^3=(A076306(1))^3 a(2)=3696 because prime(3696)+prime(3697)+prime(3698)=34603+34607+34613=47^3=(A076306(2))^3. MAPLE count:= 0: for x from 3 while count < 30 do   y:= x^3;   r:= floor(y/3);   p0:= prevprime(r); p1:= nextprime(p0); p2:= nextprime(p1);   while p0 + p1 + p2 > y do     p2:= p1;     p1:= p0;     p0:= prevprime(p0);   od:   while p0 + p1 + p2 < y do     p0:= p1;     p1:= p2;     p2:= nextprime(p2);   od:   if p0 + p1 + p2 = y then     count:= count+1;     A[count]:= numtheory:-pi(p0);   fi od: seq(A[i], i=1..count); # Robert Israel, Feb 10 2017 PROG (Python) from __future__ import division from sympy import prevprime, nextprime, isprime, primepi A158796_list, i = [], 3 while i < 10**6:     n = i**3     m = n//3     pm, nm = prevprime(m), nextprime(m)     k = n - pm - nm     if isprime(m):         if m == k:             A158796_list.append(primepi(pm))     else:         if nextprime(nm) == k:             A158796_list.append(primepi(pm))         elif prevprime(pm) == k:             A158796_list.append(primepi(pm)-1)     i += 1 # Chai Wah Wu, Jun 01 2017 CROSSREFS Cf. A076304, A076306. Sequence in context: A017801 A201799 A017748 * A201796 A093285 A011813 Adjacent sequences:  A158793 A158794 A158795 * A158797 A158798 A158799 KEYWORD nonn AUTHOR Zak Seidov, Nov 12 2009 STATUS approved

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