A157789 Primes p such that consecutive primes p < q < r < s all are additive pointer-primes A089824.

317130731, 521142283, 557010073, 1000702693, 1281321101, 1613435111, 1802692181, 2010808001, 2012656781, 2238160121, 2352422231, 3361114331, 4302122501, 4902109481, 5044120093, 6276507313, 6542906413, 7230842923

Offset: 1

Author

Zak Seidov, Mar 06 2009

Keywords

• base
• nonn

Comments

We may call these primes the additive pointer-primes of 4th order (and then A089824 are additive pointer-primes of first order).

Are there additive pointer-primes of higher than 4th order?

The only known 5th-order additive pointer-prime < 10^12 is 102342031273 (Donovan Johnson, Oct 25 2009).

The first 10 5th-order additive pointer-primes are 102342031273, 1012835563819, 1070302300183, 2350811300953, 3063433129909, 3104103122173, 3551303300933, 5262316326901, 5426670290957, 6104611400971. The first 6th-order additive pointer-prime is 63604045061911. - Giovanni Resta, Jan 14 2013

Examples

			p=317130731, q=317130757, r=317130791, s=317130823, t=317130851;
p + sod (p) = q, q + sod (q) = r, r + sod (q) = s, s + sod (s) =t;
p<q<r<s<t are consecutive primes, sod(m)=A007953(m).
		

Links

• Donovan Johnson, Table of n, a(n) for n=1..345
• Carlos Rivera, Puzzle 163. P+SOD(P), The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A007953 Digital sum (i.e., sum of digits) of m, A089824 Primes p such that the next prime after p can be obtained from p by adding the sum of the digits of p.

Extensions

a(13)-a(18) from Donovan Johnson, Oct 11 2009