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A119768 Twin prime pairs that sum to a power. 0
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

Table of n, a(n) for n=1..37.

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.

EXAMPLE

a(3)+a(4)=71+73=144.

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]<b[1]); map(z->op(z[1..2]), L);

CROSSREFS

Sequence in context: A132239 A075432 A232882 * A232878 A226681 A005808

Adjacent sequences:  A119765 A119766 A119767 * A119769 A119770 A119771

KEYWORD

easy,nonn

AUTHOR

Walter Kehowski, Jun 18 2006

STATUS

approved

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Last modified May 24 03:21 EDT 2017. Contains 286937 sequences.