A225017 -id:A225017 - cp's OEIS frontend

A225046 Position of the first occurrence of the n-th prime in A225017, or 0 if prime(n) never occurs.

2, 5, 4, 14, 6, 7, 16, 21, 23, 24, 57, 122, 32, 19, 20, 22, 186, 177, 26, 29, 27, 61, 236, 34, 160, 36, 78, 54, 194, 41, 87, 43, 44, 188, 253, 55, 118, 229, 66, 59, 70, 69, 60, 58, 569, 279, 147, 81, 610, 74, 325, 85, 101, 75, 179, 459, 369, 100, 97, 463, 91

Offset: 4

John W. Layman, Apr 25 2013

nonn

It appears that a large fraction of terms are relatively small, say a(n)<2*n, but they can be rather large. For example, prime(156)=911 occurs first at n=14424 in A225017, so a(156) = 14424.

			A225017 begins {1,1,7,1,13,11,...}, with offset 0, and the 4th prime 7 occurs for the first time at A225017(2)=7, so a(4)=2.  11 occurs for the first time at n=5, so a(5)=5.

Alois P. Heinz, Table of n, a(n) for n = 4..240

Cf. A225017.

A225039 a(1)=2, a(2)=3, for n>=3, a(n) is the n-th number which is obtained by application Eratosthenes-like sieve to sequence: odd part of digit sum of 5^m, m>=1.

Original entry on oeis.org

2, 3, 5, 7, 13, 11, 19, 23, 17, 29, 59, 61, 31, 67, 37, 41, 79, 89, 83, 53, 103, 109, 137, 149, 151, 127, 167, 43, 211, 191, 199, 97, 181, 197, 193, 241, 269, 113, 233, 257, 139, 311, 317, 293, 283, 263, 349, 409, 173, 47, 353, 419, 431, 389, 401, 439, 463, 461

Offset: 1

Vladimir Shevelev, Apr 25 2013

We conjecture that every term is prime; moreover, we conjecture that the sequence is a permutation of the sequence of all primes.

For comparison, if in the definition we replace 5^m with 13^m, then we obtain a sequence containing 25. - Vladimir Shevelev, Dec 17 2014

Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Cf. A000040, A221858, A225017, A225040, A225093, A251964, A252280, A252281, A252282, A252283.

Flatten[{{2,3,5}, DeleteDuplicates[Select[Map[#/(2^IntegerExponent[#,2] 5^IntegerExponent[#,5])&[Total[IntegerDigits[5^#]]]&, Range[2,199]], PrimeQ]]}] (* Peter J. C. Moses, Apr 25 2013 *)

More terms from Peter J. C. Moses, Apr 25 2013

A221858 a(1)=2, a(2)=3, for n>=3, a(n) is the n-th number which is obtained by application of Eratosthenes-like sieve (with removing 1's) to sequence: odd part of digit sum of 2^m, m>=1.

Original entry on oeis.org

2, 3, 7, 5, 11, 13, 19, 29, 31, 41, 37, 43, 47, 61, 59, 67, 71, 23, 17, 73, 79, 89, 109, 103, 53, 107, 113, 139, 151, 127, 137, 83, 167, 173, 181, 191, 101, 193, 223, 233, 211, 199, 229, 251, 239, 281, 277, 241, 131, 269, 263, 283, 313, 311, 349, 163, 317, 337, 331, 307

Offset: 1

Vladimir Shevelev, Apr 25 2013

We conjecture that every term is prime;
moreover, we conjecture that the sequence is a permutation of the sequence of all primes.
For comparison, if in the definition we replace 2^m with 13^m, then we obtain a sequence containing 25. - Vladimir Shevelev, Dec 07 2014

Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Cf. A000040, A225017, A225039, A225040, A225093.

Flatten[{{2,3},DeleteDuplicates[Select[Map[#/(2^IntegerExponent[#,2])&[Total[IntegerDigits[2^#]]]&,Range[3,300]],PrimeQ]]}] (* Peter J. C. Moses, Apr 25 2013 *)

More terms from Peter J. C. Moses, Apr 25 2013

A225093 a(1)=2, a(2)=3, for n>=3, a(n) is the n-th number which is obtained by application of Eratosthenes-like sieve to A225091.

Original entry on oeis.org

2, 3, 7, 13, 5, 11, 31, 43, 37, 29, 73, 79, 19, 41, 97, 59, 103, 127, 71, 157, 17, 163, 89, 23, 107, 211, 181, 241, 199, 131, 67, 101, 61, 271, 277, 149, 313, 307, 47, 367, 173, 397, 331, 409, 179, 197, 191, 457, 251, 499, 239, 233, 487, 139, 547, 523, 571, 151

Offset: 1

Vladimir Shevelev, Apr 27 2013

nonn

We conjecture that every term is prime; moreover, we conjecture that the sequence is a permutation of the sequence of all primes. - Vladimir Shevelev, Dec 17 2014

Peter J. C. Moses, Table of n, a(n) for n = 1..2000

Cf. A000040, A221858, A225017, A225039, A225040, A225091, A251964, A252280, A252281, A252282, A252283.

Flatten[{{2,3}, DeleteDuplicates[Select[Map[#/(2^IntegerExponent[#,2])&[Total[IntegerDigits[7^#]]]&, Range[200]], PrimeQ]]}] (* Peter J. C. Moses, Apr 27 2013 *)

More terms from Peter J. C. Moses, Apr 27 2013

A225040 a(n) is the position of prime(n) in A225039, and a(n)=0, if prime(n) is not in A225039.

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 9, 7, 8, 10, 13, 15, 16, 28, 50, 20, 11, 12, 14, 69, 66, 17, 19, 18, 32, 86, 21, 64, 22, 38, 26, 74, 23, 41, 24, 25, 71, 89, 27, 49, 84, 33, 30, 35, 34, 31, 29, 175, 96, 60, 39, 181, 36, 110, 40, 46, 37, 68, 138, 119, 45, 44, 139, 42, 73, 43

Offset: 1

Vladimir Shevelev, Apr 25 2013

nonn

Conjecture: All terms are positive, or equivalently, the sequence is a permutation of the positive integers.

Peter J. C. Moses, Table of n, a(n) for n = 1..1600

Cf. A225017, A225039.

a={}; n=1; While[(tmp=Position[A225039, Prime[n]]) != {}, AppendTo[a,tmp]; n++]; Flatten[a] (* Peter J. C. Moses, Apr 25 2013 *)

A225091 The odd part of the digit sum of 7^n.

Original entry on oeis.org

1, 7, 13, 5, 7, 11, 7, 25, 31, 7, 43, 49, 37, 13, 29, 1, 13, 29, 73, 79, 19, 41, 97, 85, 73, 97, 7, 91, 133, 121, 59, 115, 103, 127, 71, 157, 17, 115, 65, 17, 71, 37, 17, 169, 175, 163, 187, 175, 17, 89, 23, 217, 49, 55, 217, 107, 211, 181, 241, 211, 199, 205

Offset: 0

Vladimir Shevelev, Apr 27 2013

Conjecture: the sequence contains all primes > 3.

Peter J. C. Moses, Table of n, a(n) for n = 0..1999

Cf. A221858, A225017, A225039, A225040.

read(transforms) :
A225091 := proc(n)
    A000265(digsum(7^n)) ;
end proc: # R. J. Mathar, May 05 2013

Map[#/(2^IntegerExponent[#,2])&[Total[IntegerDigits[7^#]]]&, Range[0,99]] (* Peter J. C. Moses, Apr 27 2013 *)

a(n) = my(s = sumdigits(7^n)); s >> valuation(s, 2); \\ Michel Marcus, Dec 19 2018

a(n) = A000265(A066003(n)). - R. J. Mathar, May 05 2013

A225430 a(n) is the smallest m for which there appears for the first time a prime p which equals odd part of sum of digits of m^2.

Original entry on oeis.org

4, 7, 8, 17, 43, 83, 167, 314, 707, 836, 6833, 8167, 21886, 41833, 89437, 134164, 947617, 987917, 3143167, 3162083, 9272917, 24060133, 60827617, 434738887, 529027313, 2641873937, 5383305583, 14141757313

Offset: 1

Vladimir Shevelev, May 07 2013

The corresponding primes are 7, 13, 5, 19, 11, 31,...

			The sequence of odd parts of sums of digits of n^2 begins 1, 1, 9, 7, 7, 9, 13, 5,... . The first appearances of primes are on places 4, 7, 8,..., so a(1) = 4, a(2) = 7, a(3)= 8, etc.

Cf. A221858, A225017, A225039, A225040, A225093.

Sort[Map[#[[1]][[2]]&,SplitBy[Sort[Select[Map[{(#/2^IntegerExponent[#,2])&[Total[IntegerDigits[#^2]]],#}&,Range[1000000]],PrimeQ[#[[1]]]&]],First]]] (* Peter J. C. Moses, May 09 2013 *)

A225516 Primes corresponding to terms of A225430.

Original entry on oeis.org

7, 13, 5, 19, 11, 31, 17, 37, 43, 23, 29, 61, 67, 73, 79, 41, 47, 97, 103, 53, 109, 59, 127, 139, 71, 151, 157, 163

Offset: 1

Vladimir Shevelev, May 09 2013

nonn

It is a result of application of Eratosthenes-like sieve to sequence of odd parts of sums of digits of n^2 which begins 1,1,9,7,7,9,13,5,... .

Conjecture: the sequence is a permutation of all primes > 3.

Cf. A221858, A225017, A225039, A225040, A225093, A225430.

cp's OEIS Frontend

A225046 Position of the first occurrence of the n-th prime in A225017, or 0 if prime(n) never occurs.

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A225039 a(1)=2, a(2)=3, for n>=3, a(n) is the n-th number which is obtained by application Eratosthenes-like sieve to sequence: odd part of digit sum of 5^m, m>=1.

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A221858 a(1)=2, a(2)=3, for n>=3, a(n) is the n-th number which is obtained by application of Eratosthenes-like sieve (with removing 1's) to sequence: odd part of digit sum of 2^m, m>=1.

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A225093 a(1)=2, a(2)=3, for n>=3, a(n) is the n-th number which is obtained by application of Eratosthenes-like sieve to A225091.

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A225040 a(n) is the position of prime(n) in A225039, and a(n)=0, if prime(n) is not in A225039.

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A225091 The odd part of the digit sum of 7^n.

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A225430 a(n) is the smallest m for which there appears for the first time a prime p which equals odd part of sum of digits of m^2.

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A225516 Primes corresponding to terms of A225430.

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