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 A319706 Filter sequence which for primes p records the prime signature of 2p+1, and for all other numbers assigns a unique number. 4
 1, 2, 2, 3, 2, 4, 5, 6, 7, 8, 2, 9, 10, 11, 12, 13, 5, 14, 5, 15, 16, 17, 2, 18, 19, 20, 21, 22, 2, 23, 24, 25, 26, 27, 28, 29, 24, 30, 31, 32, 2, 33, 5, 34, 35, 36, 5, 37, 38, 39, 40, 41, 2, 42, 43, 44, 45, 46, 5, 47, 5, 48, 49, 50, 51, 52, 53, 54, 55, 56, 5, 57, 24, 58, 59, 60, 61, 62, 5, 63, 64, 65, 2, 66, 67, 68, 69, 70, 2, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Restricted growth sequence transform of function f defined as f(n) = A046523(2n+1) when n is a prime, otherwise -n. For all i, j:   A305810(i) = A305810(j) => a(i) = a(j), and   a(i) = a(j) => A305800(i) = A305800(j),   a(i) = a(j) => A305978(i) = A305978(j),   a(i) = a(j) => A305985(i) = A305985(j). LINKS Antti Karttunen, Table of n, a(n) for n = 1..100000 PROG (PARI) up_to = 100000; rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; }; A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523 A319706aux(n) = if(isprime(n), A046523(n+n+1), -n); v319706 = rgs_transform(vector(up_to, n, A319706aux(n))); A319706(n) = v319706[n]; CROSSREFS Cf- A046523, A305800, A305810, A305900, A305901, A305978, A305985. Cf. A005384 (positions of 2's), A234095 (positions of 5's). Sequence in context: A304105 A305978 A305985 * A305894 A305811 A239471 Adjacent sequences:  A319703 A319704 A319705 * A319707 A319708 A319709 KEYWORD nonn AUTHOR Antti Karttunen, Sep 26 2018 STATUS approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)