A088602 Number of primes obtained by prefixing a single (nonzero) digit to 2n-1.

5, 6, 0, 5, 5, 4, 3, 0, 2, 4, 3, 3, 0, 4, 3, 4, 3, 0, 3, 5, 4, 3, 0, 4, 3, 3, 4, 0, 6, 3, 3, 5, 0, 4, 3, 3, 4, 0, 5, 3, 3, 5, 0, 4, 1, 4, 3, 0, 4, 3, 3, 1, 0, 3, 5, 4, 3, 0, 2, 5, 4, 3, 0, 3, 3, 4, 4, 0, 2, 5, 4, 3, 0, 4, 3, 3, 4, 0, 5, 3, 4, 5, 0, 3, 4, 3, 3, 0, 5, 2, 2, 5, 0, 5, 1, 4, 3, 0, 4, 2, 3, 2, 0, 3, 6

Offset

1,1

Comments

a(5k+3) = 0. The maximum value of a(n) is 6. If digits 1 to 9 are prefixed to 2n-1, exactly 3 numbers == 0 (mod 3). e.g. If (2n-1) == 0 (mod 3) then these are obtained on prefixing 3, 6 and 9. If (2n-1) == 1 (mod 3) then these are obtained on prefixing 2, 5 and 8. If (2n-1) == 2 (mod 3) then these are obtained on prefixing 1, 4 and 7.

Subsidiary sequences: (i) Start of the first occurrence of n successive zeros in this sequence. In the following subsequences the occurrence of a zero in between is to be neglected. (As a(3) onwards every fifth term is zero.) (ii) Start of the first occurrence of n successive ones in this sequence. etc. up to 6. (iii) Index of occurrence of 6. (iv)Index of occurrence of 5. etc.

Links

Table of n, a(n) for n=1..105.

Example

a(10) = 4, 19 = 2*10-1, the four primes are 419, 619, 719, 919.

Crossrefs

Sequence in context: A178591 A179588 A092161 * A194347 A021869 A340319

Adjacent sequences: A088599 A088600 A088601 * A088603 A088604 A088605

Keyword

base,nonn

Author

Amarnath Murthy, Oct 15 2003

Extensions

More terms from Anne M. Donovan (anned3005(AT)aol.com), Nov 05 2003

Status

approved