A154804 -id:A154804 - cp's OEIS frontend

A154799 Records in A154804.

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 19, 20, 21, 24, 28, 31, 33, 41, 42, 44, 52, 58, 69, 73, 76, 83, 92, 98, 115, 129, 138, 139, 154, 164, 165, 166, 172, 190, 198, 218, 223, 241, 268, 274, 292, 304, 330, 331, 341, 362, 394, 434, 447, 448, 466, 478

Offset: 1

Omar E. Pol, Feb 01 2009

nonn

Michael S. Branicky, Table of n, a(n) for n = 1..207

Cf. A008578, A154804, A154720, A154721.

read("transforms") ; A008578 := proc(n) RETURN( n=1 or isprime(n) ) ; end : A154804 := proc(n) local a,d; a := 0 ; for d from 1 to n-1 do if A008578(n-d) and A008578(n+d) then a := a+1; fi; od: a ; end: a804 := [seq(A154804(n),n=1..5000)] ; r := RECORDS(a804)[1] ; # R. J. Mathar, Mar 14 2009

More terms from R. J. Mathar, Mar 14 2009

a(53) and beyond from Michael S. Branicky, Dec 11 2024

A154891 Where records occurs in A154804.

Original entry on oeis.org

1, 2, 4, 9, 12, 21, 24, 30, 42, 45, 57, 60, 75, 84, 90, 105, 135, 150, 165, 195, 210, 255, 315, 330, 390, 420, 525, 630, 735, 825, 840, 945, 1050, 1155, 1365, 1575, 1680, 1785, 1995, 2100, 2145, 2205, 2310, 2625, 2730, 3045, 3255, 3465, 3990, 4095, 4515, 4620

Offset: 1

Omar E. Pol, Feb 01 2009

nonn

Michael S. Branicky, Table of n, a(n) for n = 1..207

Cf. A008578, A154804, A154720, A154721, A154799.

A008578 := proc(n) RETURN( n=1 or isprime(n) ) ; end : A154804 := proc(n) local a,d; a := 0 ; for d from 1 to n-1 do if A008578(n-d) and A008578(n+d) then a := a+1; fi; od: a ; end: a804 := [seq(A154804(n),n=1..4000)] ; r := RECORDS(a804)[2] ; # R. J. Mathar, Mar 14 2009

More terms from R. J. Mathar, Mar 14 2009

a(50) and beyond from Michael S. Branicky, Dec 11 2024

A341973 Number of partitions of n into 2 distinct primes (counting 1 as a prime).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 2, 0, 3, 1, 3, 1, 2, 0, 4, 1, 2, 0, 2, 0, 4, 1, 3, 1, 3, 0, 4, 0, 2, 1, 3, 0, 5, 1, 4, 1, 3, 0, 6, 1, 4, 0, 3, 0, 6, 1, 3, 0, 3, 0, 7, 1, 3, 1, 5, 0, 6, 0, 3, 1, 5, 0, 7, 1, 5, 1, 5, 0, 7, 0, 5, 1, 4, 0, 9, 1, 4, 0, 4, 0, 10, 1, 4, 0, 4, 0, 7

Offset: 3

Ilya Gutkovskiy, Feb 24 2021

nonn

Alois P. Heinz, Table of n, a(n) for n = 3..10000

Cf. A008578, A036497, A117929, A154804, A341945, A341974, A341975, A341976, A341977.

b:= proc(n, i) option remember; series(`if`(n=0, 1,
     `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i-1)))(
     `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 3)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 2):
seq(a(n), n=3..96);  # Alois P. Heinz, Feb 24 2021

a[n_] := Select[IntegerPartitions[n, {2}, Join[{1},
    Prime[Range[PrimePi[n-1]]]]], #[[1]] != #[[2]]&] // Length;
a /@ Range[3, 100] (* Jean-François Alcover, Jul 13 2021 *)

a(n) = A117929(n) + A010051(n-1). - R. J. Mathar, Oct 01 2021

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A154799 Records in A154804.

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A154891 Where records occurs in A154804.

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A341973 Number of partitions of n into 2 distinct primes (counting 1 as a prime).

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