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 A245815 Permutation of natural numbers induced when A245821 is restricted to nonprime numbers: a(n) = A062298(A245821(A018252(n))). 5
 1, 2, 5, 3, 4, 7, 9, 59, 11, 6, 20, 125, 18, 25, 15, 10, 16, 26, 32, 31, 103, 8, 12, 35, 41, 50, 13, 39, 85, 64, 43, 164, 29, 38, 17, 66, 19, 24, 21, 45, 132, 37, 105, 139, 82, 33, 65, 27, 507, 52, 14, 180, 161, 96, 46, 22, 190, 141, 87, 1603, 80, 36, 143, 107, 54, 670, 34, 47, 23, 68, 177, 1337, 40 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This permutation is induced when A245821 is restricted to nonprimes, A018252, the first column of A114537, but equally, when it is restricted to column 2 (A007821), column 3 (A049078), etc. of that square array, or alternatively, to the successive rows of A236542. The sequence of fixed points f(n) begins as 1, 2, 15, 142, 548, 1694, 54681. A018252(f(n)) gives the nonprime terms of A245823. LINKS Antti Karttunen, Table of n, a(n) for n = 1..10001 FORMULA a(n) = A062298(A245821(A018252(n))). As a composition of related permutations: a(n) = A245813(A245819(n)). Also following holds for all n >= 1: a(n) = A062298(A049084(A245821(A007821(n)))). a(n) = A062298(A049084(A049084(A245821(A049078(n))))). PROG (PARI) allocatemem(234567890); v014580 = vector(2^18); v091226 = vector(2^22); v091242 = vector(2^22); isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV i=0; j=0; n=2; while((n < 2^22), if(isA014580(n), i++; v014580[i] = n; v091226[n] = v091226[n-1]+1, j++; v091242[j] = n; v091226[n] = v091226[n-1]); n++); A002808(n)={my(k); for(k=0, primepi(n), isprime(n++)&&k--); n}; \\ This function from M. F. Hasler A062298(n) = n-primepi(n); A018252(n) = if(1==n, 1, A002808(n-1)); A014580(n) = v014580[n]; A091226(n) = v091226[n]; A091242(n) = v091242[n]; A091205(n) = if(n<=1, n, if(isA014580(n), prime(A091205(A091226(n))), {my(irfs, t); irfs=subst(lift(factor(Mod(1, 2)*Pol(binary(n)))), x, 2); irfs[, 1]=apply(t->A091205(t), irfs[, 1]); factorback(irfs)})); A245703(n) = if(1==n, 1, if(isprime(n), A014580(A245703(primepi(n))), A091242(A245703(n-primepi(n)-1)))); A245821(n) = A091205(A245703(n)); A245815(n) = A062298(A245821(A018252(n))); for(n=1, 10001, write("b245815.txt", n, " ", A245815(n))); (Scheme) (define (A245815 n) (A062298 (A245821 (A018252 n)))) CROSSREFS Inverse: A245816. Related permutations: A245813, A245819, A245821. Cf. A007821, A018252, A049078, A062298, A114537, A236542, A245823. Sequence in context: A065181 A026258 A105530 * A105108 A118460 A064788 Adjacent sequences:  A245812 A245813 A245814 * A245816 A245817 A245818 KEYWORD nonn AUTHOR Antti Karttunen, Aug 02 2014 STATUS approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)