A147568 -id:A147568 - cp's OEIS frontend

A152259 Union of values: A147568(n) and 2*A147568(n) - 1.

3, 5, 9, 11, 13, 21, 25, 35, 37, 43, 45, 69, 73, 85, 89, 131, 133, 139, 141, 163, 165, 171, 173, 261, 265, 277, 281, 325, 329, 341, 345, 515, 517, 523, 525, 547, 549, 555, 557, 643, 645, 651, 653, 675, 677, 683, 685, 1029, 1033, 1045, 1049, 1093, 1097, 1109, 1113, 1285, 1289

Offset: 1

Vladimir Shevelev, Dec 01 2008

nonn

Every even N>=6 is a sum of two terms of the sequence.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A000695, A145812, A145819, A147568.

A000695[n_]:= FromDigits[IntegerDigits[n,2], 4];
Table[(3+(-1)^n)*A000695[Floor[(2*n-2-(-1)^n)/4]] +4+(-1)^n , {n, 202}]//DeleteDuplicates//Sort (* G. C. Greubel, May 22 2023 *)

a147568(n) = 2*fromdigits(binary(n), 4) + 3;
lista(nn) = {my(v = vector(2*nn+2), ind = 0); for (n=0, nn, my(x = a147568(n)); v[ind++] = x; v[ind++] = 2*x - 1); vecsort(v,,8);} \\ Michel Marcus, Dec 18 2018

More terms from Michel Marcus, Dec 18 2018

Missing term 685 added by G. C. Greubel, May 22 2023

A153401 a(n) is the least positive number such that in the representation of 2n+1, n>=4, as a sum of the form (2A000695(k)+a(n))+2(2A000695(l)+a(n)), both of numbers 2A000695(k)+a(n) and 2A000695(l)+a(n) are primes.

Original entry on oeis.org

1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 7, 3, 9, 1, 1, 5, 3, 7, 9, 3, 7, 1, 1, 19, 3, 0, 5, 7, 3, 3, 5

Offset: 4

Vladimir Shevelev, Dec 25 2008

For a given c>=3, every odd N>=3c is a unique sum of the form (2*A000695(k)+c) +2(2*A000695(l)+c).

Cf. A046927, A103151, A000695, A145812, A147568.

cp's OEIS Frontend

A152259 Union of values: A147568(n) and 2*A147568(n) - 1.

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A153401 a(n) is the least positive number such that in the representation of 2n+1, n>=4, as a sum of the form (2A000695(k)+a(n))+2(2A000695(l)+a(n)), both of numbers 2A000695(k)+a(n) and 2A000695(l)+a(n) are primes.

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cp's OEIS Frontend

A152259 Union of values: A147568(n) and 2*A147568(n) - 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A153401 a(n) is the least positive number such that in the representation of 2n+1, n>=4, as a sum of the form (2*A000695(k)+a(n))+2(2*A000695(l)+a(n)), both of numbers 2*A000695(k)+a(n) and 2*A000695(l)+a(n) are primes.

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Author

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A153401 a(n) is the least positive number such that in the representation of 2n+1, n>=4, as a sum of the form (2A000695(k)+a(n))+2(2A000695(l)+a(n)), both of numbers 2A000695(k)+a(n) and 2A000695(l)+a(n) are primes.