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 A119768 Twin prime pairs that sum to a power. 4
 3, 5, 17, 19, 71, 73, 107, 109, 881, 883, 1151, 1153, 2591, 2593, 3527, 3529, 4049, 4051, 15137, 15139, 20807, 20809, 34847, 34849, 46817, 46819, 69191, 69193, 83231, 83233, 103967, 103969, 112337, 112339, 139967, 139969, 149057, 149059, 176417 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Since twin prime pairs greater than (3,5) occur as either (5,7) mod 12 or (11,1) mod 12, all sums of such twin primes are always divisible by 12. Thus all powers are divisible by 12. The first few terms in base 12 are: 15, 17, 5E, 61, 8E, 91, 615, 617, 7EE, 801, 15EE, 1601 and the corresponding powers are 30, 100, 160, 1030, 1400, 3000. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA If a(n) is the above sequence of twin primes, then a(2n-1),a(2n) is a twin prime pair and a(2n-1)+a(2n) is a power. a(2*n-1) = A270231(n), a(2*n) = A270231(n) + 2. - Amiram Eldar, Jan 05 2020 EXAMPLE a(5) + a(6) = 71 + 73 = 144 = 12^2. MAPLE egcd := proc(n::nonnegint) local L; if n=0 or n=1 then n else L:=ifactors(n)[2]; L:=map(z->z[2], L); igcd(op(L)) fi end: L:=[]: for w to 1 do for x from 1 to 2*12^2 do s:=6*x; for r from 2 to 79 do t:=s^r; if egcd(s)=1 and andmap(isprime, [(t-2)/2, (t+2)/2]) then print((t-2)/2, (t+2)/2, t)); L:=[op(L), [(t-2)/2, (t+2)/2, t]]; fi; od od od; L:=sort(L, (a, b)->a[1]op(z[1..2]), L); MATHEMATICA powQ[n_] := GCD @@ FactorInteger[n][[;; , 2]] > 1; aQ[n_] := PrimeQ[n] && PrimeQ[n + 2] && powQ[2 n + 2]; s = Select[Range[10^4], aQ]; Union @ Join[s, s + 2] (* Amiram Eldar, Jan 05 2020 *) PROG (PARI) my(pp=3); forprime(p=5, 180000, if(p-pp==2, if(ispower(p+pp), print1(pp, ", ", p, ", "))); pp=p) \\ Hugo Pfoertner, Jan 05 2020 CROSSREFS Cf. A001097, A001359, A006512, A069496, A270231, A330978, A330980. Sequence in context: A045416 A038891 A287638 * A020592 A295387 A263258 Adjacent sequences:  A119765 A119766 A119767 * A119769 A119770 A119771 KEYWORD easy,nonn,tabf AUTHOR Walter Kehowski, Jun 18 2006 EXTENSIONS a(1)-a(2) inserted by Amiram Eldar, Jan 05 2020 STATUS approved

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)