A059755 Odd rare numbers: odd n such that n-r and n+r are squares, where r is the reverse of n.

65, 868591084757, 6979302951885, 6157577986646405, 8052956026592517, 8052956206592517, 8650327689541457, 8650349867341457, 619431353040136925, 619631153042134925, 631688638047992345, 633288858025996145, 633488632647994145, 653488856225994125

Offset: 1

Author

Shyam Sunder Gupta, Feb 11 2001

Keywords

• nice
• nonn
• base

Comments

There are 20 terms up to 10^22. - Shyam Sunder Gupta, Dec 14 2019

Examples

			65-56 = 9 and 65 + 56 = 121 are both (perfect) squares.
		

References

• Shyam Sunder Gupta, "Systematic computations of rare numbers", The Mathematics Education, Vol. XXXII, No. 3, 1998.

Links

• Shyam Sunder Gupta, Table of n, a(n) for n = 1..20
• Carlos Rivera, Conjecture 23. The Shyam's conjecture about the Rare Numbers, The Prime Puzzles & Problems Connection.
• Shyam Sunder Gupta, Rare Numbers
• Shyam Sunder Gupta, Rare Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 14, 381-397. {{doi|10.1007/978-981-97-2465-9_14}}

Crossrefs

Cf. A035519.