A277854 -id:A277854 - cp's OEIS frontend

A277852 "Late birds" (values a(n) < a(k) for all k > n) in A075771 = quotient + remainder of Euclidean division of n^2 by prime(n).

1, 2, 4, 5, 9, 15, 16, 24, 59, 61, 81, 100, 124, 129, 152, 169, 196, 249, 305, 400, 425, 475, 520, 556, 565, 676, 771, 795, 904, 939

Offset: 1

M. F. Hasler, Nov 25 2016

The lower bound A075771(n) >= n^2/prime(n) ensures that a given number can't occur beyond a certain index in that sequence.

See A277853 for the corresponding indices m.

Cf. A075771, A277851, A277853, A277854.

A277852(N,L=N^2/prime(N),A=A075771,S=List())={forstep(n=N,1,-1,A(n)

a(n) = A075771(A277853(n)), i.e., equals A075771 o A277853.

A277853 Indices m of "late birds", i.e., values a(m) < a(k) for all k > m, in A075771 = quotient + remainder in Euclidean division of n^2 by prime(n).

Original entry on oeis.org

1, 2, 4, 5, 21, 27, 44, 104, 173, 365, 369, 500, 590, 735, 840, 987, 1564, 1797, 2415, 3368, 3545, 4025, 4466, 5018, 5477, 6686, 7239, 8025, 8182, 9369

Offset: 1

M. F. Hasler, Nov 25 2016

See A277852 (= A075771 o A277853) for the corresponding values of the "late birds".

Cf. A075771, A277851, A277852, A277854.

A277853(N,L=N^2/prime(N),A=A075771,S=List())={forstep(n=N,1,-1,A(n)

A277851 Numbers not occurring in A075771 (= q(n) + r(n), with n^2 = prime(n)*q(n) + r(n), 0 <= r(n) < prime(n)).

Original entry on oeis.org

3, 6, 7, 8, 11, 13, 14, 18, 19, 20, 21, 22, 23, 25, 26, 29, 30, 32, 34, 35, 38, 39, 40, 43, 44, 45, 47, 51, 53, 54, 56, 58, 62, 67, 68, 69, 70, 71, 72, 74, 75, 77, 78, 80, 82, 83, 87, 89, 90, 91, 92, 94, 97, 98, 99, 102, 103, 104, 105, 106, 107, 108, 110, 111, 112, 115, 117, 118, 119, 120, 122, 123, 125, 126

Offset: 1

M. F. Hasler, Nov 25 2016

nonn

The lower bound A075771(n) >= n^2/prime(n) ensures that a given number can't occur beyond a certain index in that sequence.

Cf. A075771, A277852, A277853, A277854.

mx = 6300; Take[ Complement[ Range@ mx, Array[Plus @@ IntegerDigits[#^2, Prime[#]] &, mx]], mx/90] (* Robert G. Wilson v, Nov 25 2016 *)

A277851_vec(N,L=N^2\prime(N),A=A075771)=setminus([1..L],Set(vector(N,n,A(n))))

cp's OEIS Frontend

A277852 "Late birds" (values a(n) < a(k) for all k > n) in A075771 = quotient + remainder of Euclidean division of n^2 by prime(n).

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A277853 Indices m of "late birds", i.e., values a(m) < a(k) for all k > m, in A075771 = quotient + remainder in Euclidean division of n^2 by prime(n).

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A277851 Numbers not occurring in A075771 (= q(n) + r(n), with n^2 = prime(n)*q(n) + r(n), 0 <= r(n) < prime(n)).

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PARI