A290425 Primes p such that the reverse of 4*p is the nextprime(p+1).

23, 233, 2333, 23333, 233217800219782199997821978002178083, 233002199978219997802199978219997800083, 233219782178000217802178000217821978083, 2330000000002178217821782178000000000083, 2330217821780219999999999780217821780083, 233000000002197802178217802197800000000083, 233000002199978021978219780219997800000083

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

Max Alekseyev, Table of n, a(n) for n = 1..56887

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

(PARI) 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 A362431

Adjacent sequences: A290422 A290423 A290424 * A290426 A290427 A290428

Keyword

nonn,base

Author

David James Sycamore, Jul 31 2017

Extensions

Missing terms a(5) onward added by Max Alekseyev, May 22 2026

Status

approved