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A290425 Primes p such that the reverse of 4*p is the nextprime(p+1). 0
23, 233, 2333, 23333 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From David A. Corneth, Aug 02 2017: (Start)

23333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 is a term.

Terms start with 2 and end in 3. Proof (for base 10):

Let d[1] be the first digit of term p. Then 1 <= d[1] <= 9. Let r be the reverse of 4*p. If d[1] > 2 then r is too large to be nextprime(p + 1). if p = 1 then 4*p starts with 5 or 6 i.e. r ends in 5 or 6. No terms can match these conditions so d[1] = 2. If d[1] = 2 then p ends in 3 or 8. As primes don't end in 8, p ends in 3. (End)

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

p(9)=23, 4*23=92;  29=p(10).

MATHEMATICA

Select[Prime@ Range[10^6], NextPrime@ # == IntegerReverse[4 #] &] (* Michael De Vlieger, Aug 02 2017 *)

PROG

is(n) = isprime(n) && fromdigits(Vecrev(digits(4*n))) == nextprime(n+1) \\ David A. Corneth, Aug 02 2017

CROSSREFS

Cf. A093672, A198972.

Sequence in context: A140572 A140844 A168438 * A034986 A243449 A068838

Adjacent sequences:  A290422 A290423 A290424 * A290426 A290427 A290428

KEYWORD

nonn,base,more

AUTHOR

David James Sycamore, Jul 31 2017

STATUS

approved

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Last modified March 30 09:49 EDT 2020. Contains 333125 sequences. (Running on oeis4.)