A302847 -id:A302847 - cp's OEIS frontend

A302848 Permutation of natural numbers: a(1) = 1; for n > 1, a(n) = 1+A064989(A003961(n)-2).

1, 2, 3, 6, 4, 12, 5, 10, 20, 18, 8, 42, 7, 30, 15, 74, 14, 72, 11, 60, 48, 32, 9, 86, 44, 26, 75, 90, 24, 102, 16, 240, 21, 22, 19, 212, 23, 62, 80, 92, 38, 158, 13, 58, 168, 40, 27, 320, 66, 70, 59, 150, 35, 368, 84, 160, 110, 56, 54, 312, 34, 108, 111, 720, 45, 192, 39, 122, 78, 228, 68, 662, 36, 50, 33, 112, 87, 134, 17, 328, 416, 114, 47, 300, 128

Offset: 1

Antti Karttunen, Apr 26 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..20000
David Newman, et al., New sequences from old, Discussion on SeqFan-mailing list, January 2018.
Index entries for sequences that are permutations of the natural numbers
Index entries for sequences computed from indices in prime factorization

Cf. A302847 (inverse).

Cf. A003961, A048673, A064216, A064989, A302850.

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A302848(n) = if(1==n,n,1+A064989(A003961(n)-2));

a(1) = 1; for n > 1, a(n) = 1+A064989(A003961(n)-2).

a(1) = 1; for n > 1, a(n) = 1+A064216(A048673(n)-1).

A302849 Permutation of natural numbers: a(1) = 1, a(2) = 2; for n > 2, a(n) = A064989(4+A003961(n-2)).

Original entry on oeis.org

1, 2, 3, 5, 4, 11, 7, 17, 6, 29, 23, 9, 13, 25, 10, 31, 22, 39, 19, 73, 8, 61, 53, 41, 14, 137, 47, 21, 82, 101, 15, 107, 37, 187, 38, 59, 16, 227, 12, 71, 83, 191, 43, 121, 26, 49, 173, 55, 34, 401, 27, 149, 28, 151, 20, 373, 51, 205, 65, 89, 33, 161, 67, 57, 116, 727, 74, 197, 18, 45, 139, 129, 35, 445, 79, 113, 158, 199, 50, 155, 46, 569, 403, 85, 58

Offset: 1

Antti Karttunen, Apr 26 2018

nonn

Cf. A302850 (inverse).

Cf. A003961, A064989, A302847.

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A302849(n) = if(n<=2,n,A064989(4+A003961(n-2)));

a(1) = 1, a(2) = 2; for n > 2, a(n) = A064989(4+A003961(n-2)).

A354964 a(1) = 1, a(2) = 2, a(3) = 3; for n > 3, a(n) is the smallest new number such that the sum of any four successive terms is prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 4, 13, 17, 9, 8, 19, 11, 15, 14, 21, 23, 25, 10, 31, 35, 27, 16, 29, 37, 45, 20, 47, 39, 33, 12, 43, 49, 53, 6, 41, 51, 59, 22, 61, 55, 73, 34, 65, 57, 67, 38, 71, 63, 69, 24, 77, 81, 75, 18, 83, 87, 89, 48, 93, 101, 95, 28

Offset: 1

Zak Seidov, Jun 13 2022

nonn

Cf. A080164, A336816, A302847.

See A055265 and A076990 for similar sequences.

s = {1, 2, 3}; Do[a = s[[-1]] + s[[-2]] + s[[-3]]; n = 4; While[MemberQ[s, n] || ! PrimeQ[a + n], n++]; AppendTo[s, n], {120}]; s

{ s = 0; for (n=1, #a = vector(62), if (n<=3, a[n]=n, for (v=1, oo, if (!bittest(s,v) && isprime(v+a[n-1]+a[n-2]+a[n-3]), a[n]=v; break))); print1 (a[n]", "); s+=2^a[n]) } \\ Rémy Sigrist, Jul 03 2022

cp's OEIS Frontend

A302848 Permutation of natural numbers: a(1) = 1; for n > 1, a(n) = 1+A064989(A003961(n)-2).

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A302849 Permutation of natural numbers: a(1) = 1, a(2) = 2; for n > 2, a(n) = A064989(4+A003961(n-2)).

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Formula

A354964 a(1) = 1, a(2) = 2, a(3) = 3; for n > 3, a(n) is the smallest new number such that the sum of any four successive terms is prime.

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